Derivation of governing equations for multiphase flows with arbitrary number of phases in deformable porous media on the basis of thermodynamically compatible systems theory is presented. Numerical modelling of the nonlinear multiphase filtration is based on the finite volume method and using WENO reconstruction of initial data in combination with Runge-Kutta method. Simulation was performed for non-linear non-isothermal filtration of the oil-water mixture through the deformable porous medium.