[en] A spherical plasma cloud generated by a vacuum are, is considered as expanding in an ambient neutral gas in a self-similar approximation. Under the assumption that the cathode erosion rate as well as density of the ambient neutral gas are constant during the plasma expansion, the self-similarity parameter is A = (1/ρ³dM/dt)^1/3 where ρ³ is the density of undisturbed gas, M is the mass of the expanding metal vapor, and t is time, while the dimensionless independent variable is ξ = r/At^1/3, where r is the distance from the cloud center. The equations of plasma motion and continuity are: ∂v/∂t + ∂n/∂r +1∂p/ρ∂r = 0 ∂ρ/∂t + ∂ρ/∂r + ρ(∂v/∂r + 2v/r) = 0 where v, ρ, P are plasma velocity, density and pressure, transformed in the self-similar form and solved numerically. Boundary conditions were formulated on the front of the plasma expansion taking into account that 1) the front edge of the shock wave expanding in the ambient neutral gas and 2) the rate of cathode erosion is a constant. For an erosion rate of 104 g/C, a cathode ion current of about 20 A and an ambient gas pressure about 0.1 Torr, the radius of the plasma cloud is r (m) = 0.834 x t^1/3. At t = 10^-5s, the plasma cloud radius is about 0.018 m, while the front velocity is v_f = 600 m/s