A particle code is used to simulate the evolution of a magnetic slow shock. The initial state is two uniform plasmas related by the Rankine-Hugoniot jump conditions and separated by a transition layer a few ion gyroradii thick. The code follows the evolution of the system in time. Two principal features of the results are the upstream escape of the hot shocked plasma and a damped, left-handed circularly polarized wave on the trailing edge of the shock. Analysis of the trailing wave train indicates that ion cyclotron interaction is important in heating the plasma. The upstream escape of particles results in a temporal broadening of the shock profile. The implications of the simulation results in magnetic merging processes in the neighborhood of an x type neutral point are described.