We use a newly developed 2-D electrostatic code with particle ions and Boltzmann electrons to investigate the details of the ion/ion acoustic instability and the structure of electrostatic shocks. The ion/ion acoustic instability is thought to be operative in various regions of space plasmas, such as the plasma sheet boundary layer or the bow shock. Electrostatic shocks have also been hypothesized to exist in a variety of physical settings, such as the inner cometary coma or the auroral region. The simulation results show that for the parameters relevant to the plasma sheet boundary layer the saturation mechanism of the ion/ion acoustic instability is ion trapping. We also show that the 2-D structure of electrostatic shocks is considerably different from that suggested by previous 1-D simulations. The main reason for this difference is the presence of shock reflected ions, which through the ion/ion acoustic instability lead to the generation of large amplitude waves in the upstream region propagating obliquely to the shock normal. These waves play an important role in the shock dissipation process. ¿ American Geophysical Union 1991