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The aim of this paper is to quantify uncertainty of flow in porous media through stochastic modeling and computation of statistical moments. The governing equations are based on Darcy’s law with stochastic permeability. Starting from a specified covariance relationship, the log permeability is decomposed using a truncated Karhunen–Loève expansion. Mixed finite element approximations are used in the spatial domain and collocation at the zeros of tensor product Hermite polynomials is used in the stochastic dimensions. Error analysis is performed and experimentally verified with numerical simulations. Computational results include incompressible and slightly compressible single and two-phase flow.