Based on the method of obtaining the partial derivatives of basic random variables, stochastic boundary integral equations are established, and practically, the method is applied to resolve the engineering problems of concrete gravity dams, considering the random factors including material parameters of dam body, water level of upper reaches, anti-slide friction coefficient of dam base, etc. Numerical examples show that the stochastic boundary element method applied in the paper, to compute the reliability degree of grand volume constructions such as concrete gravity dam, comparatively has the advantage of inputting fewer data and its computational results are more precise.