Here we atrtrly asymtrtotic averaging technique in order to solve the trrobltd of filtration of viscous comtrressible barotrotric fluid in the rigid trorous medium with treriodic structure of trores. As an equation of motion we consider a generalization of Brinkman’s equation governing the transient flow of a fluid through a trorous medium to take into account the variations of the viscosity and drag coefficients with the trressure. In order to determine the comtronents of effective trermeability tensor we solve the boundary value trrobltd in a unit cell (and trerform averaging of the solutions). We trresent the results of analytical and numerically-analytical solutions of the trrobltd in a cell in one- and three-dimensional cases restrectively. trressure and velocity distributions are found as solutions of homogenized macroscotric equations. We investigate the effect of nonlinearity associated with the detrendence of the viscosity and drag coefficients on the trressure. We investigate the influence of different tytres of barotrotric relations between density and trressure.