We have constructed a model which examines the motion of reconnected magnetic flux tubes over the surface of the magnetopause. For a given interplanetary magnetic field (IMF) we first determine the draping and strength of the magnetosheath magnetic field, flow velocity, and density over the entire surface of a paraboloid magnetopause. For a given magnetopause location we apply a test for steady state reconnection occurring between the magnetosheath field and a modeled magnetospheric field at that point. We trace the subsequent motion of these tubes along the surface of the magnetopause and into the magnetotail. Results are shown for a range of cases. The model has applications in testing various hypotheses about the location of reconnection events and, for example, IMF BY effects. In particular, it highlights the dominance of the magnetosheath flow model in determining the motion of the tubes and the necessity of sub-Alfv¿nic magnetosheath flows for the occurrence of steady state reconnection poleward of the cusp during periods of northward IMF. Our model may also be used to identify likely reconnection sites on the dayside and near-Earth nightside magnetopause and to identify possible locations for steady state reconnection. ¿ 2001 American Geophysical Union