For massive concrete structures such as concrete gravity dams, the materials have random spatial distribution properties due to the influences of raw materials and their mixing, as well as the pouring construction. Using the discretization theory of the local average method for a stationary random field, a computational formula of the structural random response for gravity dams is derived based on Neumann expansion stochastic finite element. Corresponding calculation method for the reliability of gravity dams is proposed together with a programmed Matlab code. A cantilever beam is given for the validation of the method and the influence of element size and fluctuation scale of the random field on structural reliability is discussed. The tensile strength reliability of the dam heel is also calculated. The results show that the reliability of a dam can be influenced significantly by the fluctuation scale. Reliability increases with a decreasing fluctuation scale, and it is undervalued if the elastic modulus is considered as a single random variable. In addition, the discretized element size of the random field should be determined by the fluctuation scale and it should not be too large. The suggested element size is less than 1/10~1/8 of the fluctuation scale.