The paper investigates a mathematical model of a two-phase medium under the assumption that the phases are in equilibrium with respect to pressure and temperature. Dissipative effects are determined by interfacial friction. In the one-dimensional case, a group analysis of the dissipative system of equations for a two-phase medium is carried out. In the two-dimensional case, the system is solved numerically by the third-order TVD Runge-Kutta method. A problem of two-phase medium motion in a channel in a gravitational field is solved.