The process of flow of Solar wind plasma over the localized barrier such as the Earth magnetic field is studied by the numerical methods. The research is carried out in magnetohydrodynamic approach. Nonstationarity of such interaction is occassioned by inhomogeneities of the coming flow, transient and wave processes, which are caused by instabilities of medium movement, as well. The computer program of two-dimensional computing magnetohydrodynamic simulation was created for the research of these problems. This program allows to review quickly the one-dimensional computing dynamic process scenario for the selection of parameters. The model interaction of the Earth magnetosphere with density and velocity inhomogeneity in the Solar wind was demonstrated by the program. It was shown, that the model two-dimensional disturbance penetrates into magnetosphere region. It creates the noticeable change of the Earth magnetic field there. Problems, connected with random regimes because of time and space discrete of computing model were solved.