Analysis tools available for massive concrete technology are still limited to deterministic models, which can’t be used for the various uncertainty quantification of the structural performance. In this paper the spectral stochastic finite element (SSFEM) analysis theory of the mass concrete structures is developed. First the random field is discretized with the K-L expansion and the Galerkin approach; together with the polynomial chaos expansion (PCE) for output stochastic field, the SSFEM framework is then formulated for mechanic problems. Special items such as the reliability concerning displacement are also addressed. Practical gravity dam problem is provided as an illustration and verification.