The article discusses the problem of approximating solutions of differential equations describing the process of a two-dimensional fluid flow in porous media. The approximation is presented as a combination of radial basis functions on the basis of the Green’s function is used to solve the Poisson equation with variable coefficients in the case of steady state filtration and parabolic equations in the transient regime. To illustrate the effectiveness of the proposed approximation obtained by the field pressure distribution in the reservoir with a network of injection and production wells. Compare approximated pressure and design points to a satisfactory accuracy of the results