Exhibit 10.4

LOCK-UP AGREEMENT

This LOCK-UP AGREEMENT, as may be amended, supplemented or modified from time to time in accordance with the terms hereof, is made as September 21, 2015 (this “Agreement”) by and between TransEnterix, Inc., a Delaware corporation (the “Company”) and SOFAR, S.p.A., an Italian societa’ per azioni (the “Investor”).

WHEREAS, the Company and the Investor have entered into that certain Purchase Agreement pursuant to which the Company acquired all of the membership interests of the entity to which Investor had conferred its medical robotic division related to the advanced robotic system for minimally invasive laparoscopic surgery known as TELELAP ALF-X (the “Transaction”);

WHEREAS, in consideration for the acquisition of all of the issued and outstanding membership interests of VULCANOS S.r.l., an Italian societa’ a responsabilita’ limitata solely owned by the Investor, the Company has issued to the Investor shares of the Company’s common stock, par value $0.001 per share, equal to or less than 19.99% of the outstanding shares of the Company (the “Shares”) as a transaction under Regulation S; and

WHEREAS, as a condition and inducement to the Company entering into the Transaction and incurring the obligations set forth therein, the Investor agrees to be bound by the covenants contained in this Agreement.

NOW, THEREFORE, in consideration of the mutual covenants and agreements set forth herein and for good and valuable consideration, the receipt and adequacy of which are hereby acknowledged, the parties hereto agree as follows:

“Agreement” has the meaning set forth in the Preamble.

“Affiliate” means any Person who is an “affiliate” as defined in Rule 12b-2 promulgated under the Exchange Act.

“Board of Directors” means the Board of Directors of the Company.

“Business Day” means a day other than a Saturday, Sunday or other day on which banks located in New York, New York are authorized or required by law to close.

“Closing Date” shall mean the date as of which the Transaction has been consummated.

“Code” means the Internal Revenue Code of 1986, as amended.

“Shares” has the meaning set forth in the Recitals, provided, however, that for the avoidance of doubt Shares shall not include shares of the Company’s common stock acquired by the Investor in the open market or in any other private placement transaction occurring after the Closing Date.

“Escrow Agreement” means the Escrow Agreement entered into among the Investor, the Company and the Escrow Agent in connection with the Purchase Agreement.

“Exchange Act” means the Securities Exchange Act of 1934, as amended, and the rules and regulations promulgated thereunder.

“Investor” has the meaning set forth in the Preamble.

“Lock-up Period,” means each of (i) the period commencing on the Closing Date to and including the date that is twelve (12) months following the Closing Date (the “First Lock-up Period”); (ii) the period commencing on the Closing Date to and including the date that is eighteen (18) months following the Closing Date (the “Second Lock-up Period”); and (iii) the period commencing on the Closing Date to and including the date that is twenty-four (24) months following the Closing Date (the “Third Lock-up Period”).

“Permitted Transfer” has the meaning set forth in Section 2(c).

“Person” means any individual, firm, corporation, partnership, limited liability company, trust, incorporated or unincorporated association, joint venture, joint stock company, government (or an agency or political subdivision thereof) or other entity of any kind, and shall include any successor (by merger or otherwise) of such entity.

“Purchase Agreement” means that certain Membership Interest Purchase Agreement, dated as of September 18, 2015, among the Company, the Investor and other parties signatory thereto.

“SEC” means the U.S. Securities Exchange Commission, or any successor entity thereto.

“Securities Act” means the Securities Act of 1933, as amended, and the rules and regulations promulgated thereunder.

“Transfer” means, with respect to the Shares, the offer for sale, sale, sale of any option or contract to purchase, purchase of any option or contract to sell, grant of any option, right or warrant to purchase, or other transfer or disposition or encumbrance (or any transaction or device that is designed to or could be expected to result in the transfer or the disposition by any Person at any time in the future), whether directly or indirectly, of such Shares, and shall include the entering into of any swap, hedge or other derivatives transaction or other transaction that transfers to another, in whole or in part, any rights, economic benefits or consequences, or risks of ownership, including by way of settlement by delivery of such Shares or other securities in cash or otherwise or transferring, by gift or otherwise, any of the Shares to owners of the Investor; provided, however, that Transfer shall not include (a) any transfer to an Affiliate of the Investor provided that such transferee agrees to be bound by the terms and restrictions of this Agreement, or (b) any pledge of, or the granting of any Encumbrance (as defined in the Purchase Agreement) on, the Shares, it being understood that the Investor shall be permitted to use all or any portion of the Shares to secure the Investor’s payment and performance of any of its

2

obligations to a third party; provided, further, however, that (i) such third party must acknowledge in writing to the Company that it takes such Encumbrance subject to all restrictions in this Agreement and, for as long as the Investor is subject to the restrictions imposed on the sale of any of the Shares by an affiliate of the Company, to the applicable U.S. securities law obligations regarding any sale of the Shares pledged, and (ii) the right to pledge the Shares or otherwise create a Encumbrance applies to the Investor and not to any Affiliate to whom Shares may be transferred under clause (a) of this definition.

3

4

“THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO A LOCK- UP AGREEMENT BETWEEN THE OWNER OF SUCH SECURITIES OF TRANSENTERIX, INC. AND THE COMPANY THAT MATERIALLY RESTRICTS THE TRANSFERABILITY OF THE SECURITIES. BY ACCEPTING ANY INTEREST IN SUCH SHARES THE PERSON ACCEPTING SUCH INTEREST SHALL BE DEEMED TO AGREE TO AND SHALL BECOME BOUND BY ALL THE PROVISIONS OF SAID AGREEMENT. A COPY OF THE AGREEMENT IS ON FILE WITH THE SECRETARY OF TRANSENTERIX, INC.”

5

TransEnterix, Inc.

635 Davis Drive

Suite 300

Morrisville, NC 27560

Telecopy No.: 919-765-8459

Attention: Todd Pope

Email: tpope@transenterix.com

With a copy to:

Ballard Spahr LLP

1735 Market Street, 51st Floor

Philadelphia, PA 19103

Telecopy: (215) 864-8999

Attention: Mary J. Mullany

Email: mullany@ballardspahr.com

SOFAR, S.p.A

Via Firenze 40

20060 Trezzano Rosa (MI), Italy

Fax: 02-90967239

Phone: 02-9093621

With a copy to:

Stefano Candela

Franzosi Dal Negro Setti

Via Brera, 5

20121 Milan, Italy

Fax: 02-80299259

Phone: 02-85909220

All such notices, demands and other communications shall be deemed to have been duly given when delivered by hand, if personally delivered; when delivered by courier, if delivered by international commercial courier service; five Business Days after being deposited in the mail, postage prepaid, if mailed; and when receipt is acknowledged, if telecopied or electronically transmitted. Any party to be given notice in accordance with this section may designate another address or Person for receipt of notices hereunder.

6

7

[Remainder of page intentionally left blank.]

8

IN WITNESS WHEREOF, the undersigned have executed, or have caused to be executed, this Lock-Up Agreement on the date first written above.

[Signature Page to Lock Up Agreement]

Exhibit A

Form of Joinder

Agreement

ACKNOWLEDGMENT AND

AGREEMENT

Joinder to Lock-Up Agreement Relating to TransEnterix, Inc. Common Stock

WHEREAS, the undersigned (the “Transferee”) wishes to receive from SOFAR, S.p.A., an Italian societa’ per azioni (the “Transferor”)                  shares, par value $0.001 per share, of common stock (the “Common Stock”) of TransEnterix, Inc., a Delaware corporation (the “Company”);

WHEREAS, the Common Stock is subject to that certain Lock-Up Agreement, dated as of September 21, 2015 and as further amended from time to time (the “Agreement”), by and between the Company and Transferor. Capitalized terms used herein and not otherwise defined are given the meaning assigned to such terms in the Agreement;

WHEREAS, the Transferee has been given a copy of the Agreement and afforded ample opportunity to read it, and the Transferee is thoroughly familiar with its terms; and

WHEREAS, pursuant to the terms of the Agreement, the Transferor may not Transfer all or any portion of the Transferor’s Common Stock unless in compliance with the Agreement and in accordance with Section 2 and Section 3 thereof. This Acknowledgment and Agreement constitutes a joinder agreement as contemplated by Section 3(a) of the Agreement.

NOW, THEREFORE, in consideration of the mutual premises contained herein and for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, and to induce the Transferor to transfer such Common Stock to the Transferee and the Company to permit such transfer, the Transferee does hereby acknowledge and agree that (i) the Transferee has been given a copy of the Agreement and ample opportunity to read it, and is thoroughly familiar with its terms, (ii) the shares of Common Stock are subject to the terms and conditions set forth in the Agreement and (iii) the Transferee shall become a party to the Agreement and shall be fully bound by, and subject to, all of the covenants, terms and conditions of the Agreement as though an original party thereto.

[Remainder of page intentionally left blank.]

A-1

Signed this      day of             , 20    ,

[Signature Page to Joinder Agreement]