The interaction between the solar wind and the outflowing plasmas from a comet has been studied by using a two-dimensional time-dependent magnetohydrodynamic (MHD) simulation. The model reproduced several features of the comet-solar wind interaction predicted by earlier theories and observed on the recent cometary probes. These include the formation of the contact surface and the cometary magnetotail. For a constant interplanetary magnetic field (IMF) the cometary plasma captures field lines which drape over the comet to form an antiparallel magnetic field configuration in the tail and a thin plasma sheet. Eventually, tail magnetic reconnection begins to occur at several points. When the IMF orientation is reversed dayside magnetic reconnection occurs at the subsolar point and a large disturbance propagates down the tail.