The surge current capability is one of the key parameters for the application of silicon carbide (SiC) Schottky barrier diode (SBD) in power converters. In this study, the surge current failure mechanism of a 650 V 4H-SiC SBD during non-repetitive surge current test is investigated. The $I-V$ measurements and microscopic observations before and after surge current failure demonstrate there are two types of failure mechanisms. Experimental and electro-thermal simulation results are combined to prove that the two different failure mechanisms originate from the varied thermal strain within the chip. This article presents the cause of surge current failure of SiC SBD and establishes a surge current failure model, which is applicable to predict and optimize the surge current capability of SiC SBD.