The mathematical modeling and the computer simulation of the filtration process of heavy liquid contamination in the sloping inhomogeneous freshwater underground reservoir are carried out when a mass transfer between its stratums is taken into account. The mathematical description of such process is done within a scheme of twophase filtration for nonintermixing liquids. The basic properties of solution of differential equations were analyzed on the boundaries where an absolute permeability has a jump. The numerical modelsand highly effective algorithms are developed in which this a priori information about the solution was used. Some examples of numerical calculations are presented.