In this talk, we present an analytical form for the effective coefficient when the heterogeneous coefficients are periodic and rapidly oscillating and can be defined as step functions describing cubic blocks (square inclusions in 2-D) and spheres (circle inclusions in 2-D). The approach leads to obtain the upscaled approximation to linear and nonlinear flow equations for such geometries. The known cases in the literature comes as particular cases of this upscaled coefficient. The new contribution involves deriving an analytical approximation for the solution of the periodic cell-problem, obtained by a two-scale asymptotic expansion of the respective heterogeneous equation. By defining a correction to such approximation, the analytical effective coefficient, the zeroth order approximation and the first order approximation for the respective solutions are readily obtained. The zeroth order approximation gives the macroscopic behavior of the flow whereas the first order approximation describes the macroscopic plus microscopic features. We demonstrate, numerically, the convergence properties of these results by applying them to linear and nonlinear problems of interest in flow in porous media, where the ratios between the main matrix and the inclusion are of 1:10, 1:100, 1:1000 and 10:1 respectively.