The work is devoted to the study of the high-speed flow around an elongated body in water at various depths in the supercavitation regime. The aim of the research is to study the state of the environment around a submerged body and the possible influence of environmental disturbances on the movement of a group of bodies. The mathematical model of a compressible medium was used based on the Navier – Stokes equations. Two-phase, turbulence and phase transition were taken into account using the Mixture model, $k-\epsilon$ equations and Singhal full cavitation model, respectively. In the work, elongated conical bodies with different cavitator diameters and streamlined by a fluid flow at different speeds were considered. The numerical results were compared with the experimental results obtained by launching bodies on a hydroballistic track at the RIAMM TSU. Numerical simulation results showed that the proposed mathematical model can accurately predict the geometric shape and dimensions of the cavity. The numerical results are also in good agreement with the semi-empirical approximation for the cavity shape. Flow calculations show that a shock-wave flow pattern is formed near the body and flow disturbances propagate to a sufficient distance. On a cavitator at the front end of the body the flow is stalled and there is a sharp decrease of pressure to the values of saturated vapor pressure behind the shock wave. The dimensions of the cavity depend on the speed and ambient pressure — a greater flow rate leads to an increase in the size of the cavity. From calculations it follows that in the case of simulating deep-water launching under the same conditions of speed, following the medium pressure increase the volume of the cavity and the area of a disturbances propagation in the medium decreases, which can positively affect the accuracy of moving a group of bodies in a  water.