Abstract: Flow through a heterogeneous porous medium in a bounded domain is investigated using a recursive perturbation scheme on the stochastic steady flow problem. Two aspects of perturbation solutions are studied: the effect of boundary conditions, and the convergence of the solution. The effect of boundary conditions for a two dimensional flow with arbitrary variation of the mean flow (allowing large gradients) is investigated using analytical expressions for the head and velocity covariance functions. Boundary conditions were decomposed into deterministic and stochastic components. First order solutions for the head and velocity covariance functions for a bounded rectangular domain are derived. The results may be used to interpret experimental data for columns or data taken where conditions do not fit the average uniform flow assumption and when processes at the boundaries influence the flow and therefore the mixing of contaminants. For the study of convergence, a closer analysis of the model used for hydraulic conductivity is necessary.