Abstract. A porous media is a complex multicomponent system. The method of constructing the mathematical models of interrelated processes in such systems is described. The capabilities of FreeFem++ package in solving the corresponding free boundary-value problems for systems of quasilinear parabolic equations using the finite-element method and parallel computing are shown.

Keywords: mathematical and computer modeling, multicomponent porous media, chemical and mechanical suffusion, filtration consolidation, heat and mass transfer, free moveable boundary, system of quasilinear parabolic equations, finite element method, FreeFem++, parallel computations.