Based on numerical modeling within a two-dimensional axisymmetric problem of hydrodynamics of ideal compressible liquid, the dynamics of cavity formation in the water behind moving cylindrical bodies, having head parts of various forms, is investigated at movement velocities from 400 to 2000 m/s. Using results of calculations and experimental data, a simple model of the studied process is offered, which is based on a problem regarding the inertial expansion of a spherical cavity in the ideal incompressible liquid. It is shown that the cavity collapse during the body movement in the liquid with counter-pressure can be accompanied by the cumulative phenomena with formation of a high-velocity liquid jet that moves after the body along its axis of symmetry.