Exhibit 5.1

[Letterhead of Sullivan & Cromwell LLP]

February 2, 2021

SVB Financial Group

3003 Tasman Drive,

Santa Clara, CA 95054.

Ladies and Gentlemen:

In connection with the registration by SVB Financial Group, a Delaware corporation (the “Company”), under the Securities Act of 1933 (the “Act”) of 750,000 depositary shares (the “Depositary Shares”), each representing a 1/100^th interest in one share of the Company’s Series B Non-Cumulative Perpetual Preferred Stock, liquidation preference of $100,000 per share (the “Preferred Shares”), evidenced by depositary receipts (the “Depositary Receipts”), issued pursuant to the Deposit Agreement, dated February 2, 2021 (the “Deposit Agreement”), among the Company, American Stock Transfer and Trust Company, LLC, as depositary (the “Depositary”), and the holders from time to time of the Depositary Receipts, we, as your counsel, have examined such corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion. Upon the basis of such examination, it is our opinion that the Preferred Shares have been validly issued and are fully paid and nonassessable, and the Depositary Receipts evidencing the Depositary Shares have been validity issued and entitle the holders thereof to the rights specified in the Depositary Receipts and the Depositary Agreement, in each case subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

In rendering the foregoing opinion, we are not passing upon, and assume no responsibility for, any disclosure in any registration statement or any related prospectus or other offering material relating to the offer and sale of the Depositary Shares.

The foregoing opinion is limited to the Federal laws of the United States, the laws of the State of New York and the General Corporation Law of the State of Delaware, and we are expressing no opinion as to the effect of the laws of any other jurisdiction.

We have relied as to certain matters on factual information obtained from public officials, officers of the Company and other sources believed by us to be responsible, and we have assumed that the Deposit Agreement has been duly authorized, executed and delivered by the Depositary, that the Depositary Receipts have been duly issued against deposit of the Preferred Shares with the Depositary in accordance with the Deposit Agreement, that the certificates evidencing the Preferred Shares and the

Depositary Receipts conform to the specimens thereof examined by us, that the Depositary Receipts have been duly executed and delivered by one of the Depositary’s authorized officers and, if necessary, have been duly countersigned by the registrar for the Depositary Receipts, that the certificate evidencing the Preferred Shares has been duly countersigned by a transfer agent and duly recorded by a transfer agent and duly registered by a registrar thereof, and that the signatures on all documents examined by us are genuine, assumptions which we have not independently verified.

We hereby consent to the filing of this opinion as an exhibit to a Current Report on Form 8-K to be filed by the Company on the date hereof and its incorporation by reference into the Registration Statement relating to the Depositary Shares and to the reference to us under the caption “Validity of Shares” in the Prospectus Supplement relating to the Depositary Shares and the Preferred Shares, dated January 26, 2021, which is a part of the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act.