The steady state fast magnetic reconnection process with small separatrix angles proposed by Pestchek (1964) and generalized by Priest and Forbes (1986) is studied by a two-dimensional incompressible magnetohydrodynamic (MHD) code. In the code a uniform tangential magnetic field and normal plasma speed are specified on the inflow boundary. On the outflow boundary the tangential flow speed and tangential magnetic field are specified to be those in the Priest-Forbes' model in order to obtain different reconnection regimes. In our simulations both a uniform and a nonuniform resistivity are used. For a nonuniform resistivity model in which the resistivity in the outflow region is highly reduced, our simulations are in many aspects consistent with those in the analytical results. A steady state magnetic reconnection configuration with small separatrix angle is obtained. The plasma is heated and accelerated by the current sheets associated with slow shocks. We also obtain various regimes predicted by Priest and Forbes for different boundary conditions on the outflow boundary which are characterized by a parameter b0. They are a weak fast-mode expansion (b0=0), slow-mode compression (b0<0), slow-mode expansion (b0≥0), and a hybrid regime of fast-mode and slow-mode expansion (0<b0<1). The width and length of the current sheet for different parameters obtained in the simulations are found to be consistent with theoretical values. When the magnetic Reynolds number or the reconnection rate given on the inflow boundary increases, the diffusion region becomes smaller. However, for cases with a uniform resistivity imposed in the simulation domain it is found that the diffusion region tends to lengthen indefinitely and no steady state configuration is obtained. Magnetic islands are usually formed at the later stage of the simulation. ¿ American Geophysical Union 1992