In this paper, a numerical solution of a profile problem of suffusion in an intrapermafrost water bearing layer is investigated. Underground water filtration occurs in the water bearing layer being in contact with frozen sandy soil. During a process of soil thawing at a certain magnitude of filtration velocity the removal of soil particles from the flow has been found to occur. A mathematical model is developed with the mass conservation equations for water, moving solids, and stationary porous skeleton along with Darcy’s law for water and moving solid particles and the equation for the intensity of suffusion flow. The setting of the problem is provided in Paragraph 1 with the following: predetermined impermeability conditions are set on a part of the boundary, and predetermined pressure conditions are set at inlet and outlet. Also, an overview of suffusion models is presented. A numerical solution of the profile problem of water and solid particles movement without porous medium deformation is elaborated in Paragraph 2. The problem is reduced to a system of three equations for the porosity, pressure of the aqueous phase and concentration of solid particles. The initial boundary value problem is considered for the model problem, and the finite difference scheme based on the alternating directions method is developed. Test calculations and validations are preformed, and pressure and velocity of the aqueous phase are evaluated. Suffusion area is estimated by the comparison of the found velocity with the critical velocity value.