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In this paper, a reliable approach based on homotopy perturbation method using sumudu transform is proposed to compute an approximate solution of the system of nonlinear differential equations governing the problem of two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability. This method is called homotopy perturbation sumudu transform method (HPSTM). The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The numerical solutions show that the proposed method is very efficient and computationally attractive. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.