This thesis aims to investigate the reconnection structure and the plasma flow at the magnetopause, both on the magnetosheath and the magnetosphere side. Ongoing magnetic reconnection is assumed and not the onset of reconnection. A reconnection structure incorporating an Alfvén discontinuity, a contact discontinuity and a slow mode shock is used. Shock jump conditions are then used to derive expressions for the magnetic field and the plasma flow on both sides of the magnetopause, as well as the angles of the different discontinuities. MATLAB is used to produce plots of the structure by varying the velocity gradient and the lowest order flow velocity.