The problem of motion of low-density deformable bodies in an atmosphere is interesting in reference to the hypothesis that the Tungussk catastrophe of 1908 resulted from atmospheric deceleration of a body of large size and low density (less than 0.01 g/cm3) [1]. Article [2] investigated the region of earth destruction caused by the shock wave formed ahead of a meteorite body. The motion of the meteorite is modeled here by explosion of a linear charge of variable cross section. Article [3] examined deceleration in an exponential atmosphere of a body whose shape and size are given functions of time. It was shown that under certain conditions the shock wave separates from the body and detaches. However, the body shape is not known beforehand, in fact, and a law for its variation can be obtained only by simultaneous consideration of flow in the shock layer, the wake, and the gas cloud. With an initial cloud velocity on the order of 40 km/sec this is a difficult problem. The present author knows of no attempt to solve the problem formulated in this way. The present paper addresses the problem of motion of a gas cloud in an exponential atmosphere with large initial velocity. The cloud gas and the atmospheric gas are assumed to be perfect and ideal. The problem is solved numerically by the direct finite-difference method of Godunov [4], using a moving mesh and isolated discontinuities. The objective of the work is to elucidate the basic aerodynamic effects arising when a low-density body enters the atmosphere.