The paper deals with the heterogeneous materials with periodic structure. It is assumed that the material holds a domains with Stokes flow and domains with filtration flow through periodic joints, cylindrical pores, or spherical inclusions, where the flow is submitted to Darcy’s law. That process is described by the Brinkman filtration equation, which can to describe the free flow and permeability. At the boundary between different phases of the multiphase flow are posed boundary conditions satisfied the perfect contact conditions for tangential velocities or Beavers-Joseph contact conditions for viscous tangential stresses which suppose break of tangential velocities. Complete asymptotic analysis of the flow of incompressible fluid in two scale porous media on the base of asymptotic homogenization technique is presented. In order to solve auxiliary problems on the cell is presented the analytically-numerical method, based on approximation of the solution by shape functions, which exactly satisfied interface conditions on boundaries between different phases. The method for the solving problems on the cell allows to define global (effective) and local characteristics of porous medium with complex internal microstructure with high precision.