The magnetic barrier is a significant fraction of the magnetosheath region where magnetic forces react back on the plasma flow. We use a magnetohydrodynamic approach to calculate the solar wind flow around the magnetosphere. The use of so-called frozen-in coordinates, where the flow lines and the magnetic field are coordinate axes, is found to be most appropriate. Numerical solutions are presented for the problem of the flow around a blunt body. The results near the magnetopause are used as input parameters for a model of the reconnection of magnetic field lines based on shock-type structures.