A theoretical solution is given of the boundary shape of a magnetosphere model in which the pressure of the magnetic field inside the boundary is balanced by the pressure of solar wind flow outside the boundary. A constant pressure is assumed present in the wake of the solar wind flow, thus resulting in a model which is closed on the night side of the earth. The solution uses accurate rather than approximate equilibrium conditions, and thus gives an accurate solution of the model situation. The results show the boundary on the night side to be closer to the earth and fatter than has been earlier sketched from qualitative considerations, and the results compare well with the observations of Explorer 10, Explorer 12, and Explorer 14.