The difficulties encountered in obtaining a solution for the regular reflection of an oblique ionizing shock wave at a wall are discussed. In general it was not possible to obtain the entire solution for the shock pattern from one dimensional flow considerations. However, in the flow region relatively far removed from the wall, a free stream region, a solution may be obtained which will give both the equilibrium and nonequilibrium fluid properties behind the incident and reflected shocks as well as the reflected wave angle. It is also shown that for the case where reaction thicknesses may be considered negligible this will be the complete solution. In order to obtain a solution for the flow across a shock wave, the conservation equations of mass, energy, and momentum are solved simultaneously with the equation of state and an expression for the ionization reaction rate. Due to the nature of the equations only a numerical solution was possible, therefore, the method is demonstrated for a particular set of initial conditions.