The article proposes mathematical models and stable numerical algorithms for solving problems of deformation and flow of water-saturated porous materials. This class of problems arises in many engineering and applied fields, from field development to biomechanics. Of particular interest are the problems of the collapse of the banks of rivers, lakes and bays of the seas due to their catastrophic impact on possible consequences, for example, blocking the riverbed, the occurrence of a tsunami on the water surface of a reservoir, etc. For the mathematical description of the stress-strain state of saturated porous media, the Biot theory of three-dimensional consolidation is used, supplemented by the kinetics of damage accumulation in the medium and the Drucker-Prager yield conditions. After the formation of the main yield surface (or crack) in the material at the moment of the beginning of the collapse, its rheological properties are presented in the form of a Bingham model with a mathematical description similar to the Navier-Stokes equations with effective viscosity. A characteristic hydrodynamic feature of the problem under consideration is the presence of a free surface. Numerical modeling of the considered problems is carried out by the finite element method. The evolution of the free surface and the occurrence of a tsunami generated by a landslide are investigated.