In this paper, a mathematical model of isothermal internal erosion without deformation of a porous medium is studied. Removal of soil particles from a flow occurs at a certain magnitude of filtration velocity. Equations of mass conservation of water, moving solids, and stationary porous skeleton along with Darcy’s law for water and moving solid particles and equation for the intensity of suffusion aquifer are used as a mathematical model of the problem. Section 1 of this paper describes the problem formulation and development of the system of equations. Results of the development are a parabolic equation for water phase saturation, elliptical equation for pressure, and equation of the first order for soil porosity. The developed model demonstrates similarity with the classical Masket – Leverett model. Assumptions describing the phase transition intensity are considered in section 2. Among other things, a brief review of internal erosion models is provided. A case of self-similar motion without consideration of gravity forces and a velocity of the solid skeleton is also investigated. An equation for concentration of soil flexible solid particles is deduced.