The generalization on a case of anisotropic porous media of Rapoport?Lis model of a diphasic filtration is given. The formula for determining the capillary pressure is represented by a scalar function of the vector argument. To assign the scalar function, the tensor of capillary pressure and a tensor inverse to the tensor of the characteristic linear sizes are introduced. It is shown that Leverett's function introduced for isotropic porous media can be generalized for anisotropic media and be assigned by a fourth-order tensor. A generalization of Leverett's function and the functions of relative phase permeabilities, accounting for the hysteresis of phase permeabilities and capillary pressure is given.
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