Abstract
The article is devoted to the consideration of a model problem, where mass flow of dark matter which takeas only gravitational interacting spherical continuous medium without pressure and with radial oppositemotion with equilibrium ascending and descending components, starting free fall from boundary of thesphere and passing through the center, stopping and fall back at the boundary of the spherical massdistribution, which give us stationary spherical-symmetric configuration of dark matter. The presence of anopposite motion makes the configuration we are considering stationary. Limited mass and dimensions ofthe dark matter distribution gives us possibility to modelling galaxy galo and dark stars. This configurationis considered in the classical gravity. As a result of the study, we obtained a singular density distribution inthe center and in the shell of sphere and corresponding velocity field with singular center. The resultingprofile can be used to construct arbitrary distributions, corresponding to the observed profiles.