The motion of the MHD nonlinear shock in the Earth’s magnetosphere is considered in the scope of magnetic hydrodynamics. This wave comes from the solar wind and is refracted into the magnetosphere, generating a fast return rarefaction wave. It has been indicated that a wave refracted into the magnetosphere is a weak fast dissipative shock, propagating in magnetospheric plasma at a velocity higher than its propagation velocity in a solar wind stream. The wave motion near the Earth-Sun line with regard to the effect of the geomagnetic field transverse component is described. In this case, shock damping follows the generalized Crussard-Landau law and a wave retains its shock character up to the plasmapause, interacting with this region when an arbitrary MHD discontinuity is disintegrated. It is stated that an MHD shock loses its shock character when moving in a strongly inhomogeneous plasma within the plasmasphere and a weak shock reflected from the plasmapause can combine with a return secondary shock in the magnetosheath, promoting the experimentally observed backward motion of the bow shock front.