In this paper, a numerical solution of a twodimensional problem of water and air movement in melting snow is presented. The equation of mass conservation for each phase, the equations of twophase filtration of Musket-Leverette for water and air, equation of energy conservation for melting snow and equation of motion of ice were used as a mathematical model. Formulation of the problem is given with the following parameters: water saturation, air temperature (above the melting temperature of ice), atmospheric air pressure, water and air velocities on the snow surface, air temperature (below the melting temperature of ice), and pressure with no water at the frozen ground surface. Among other things, an overview of snow cover models for different detail levels of physical processes is presented. Balance models of snow cover are considered, and the problem of obtaining field data is discussed. Presented numerical solution of the two-dimensional problem of water and air movement in melting snow. The problem is reduced to a system of three equations for temperature, "reduced"pressure and saturation of a water phase. The obtained system of equations is considered to be an initial-boundary value problem, and the finite-difference scheme based on the alternating directions method is elaborated. Test calculations and validation are performed with saturation and temperature defined for given initial approximations. Graphical analysis of the obtained results is described. Also, finite perturbation velocity for water saturation is estimated.