The study of the transition from regular to Mach reflection of shock waves has received considerable attention over the past decade, particularly because of the differences found between numerical and experimental data sets. Whereas this has now been satisfactorily shown to be due to wind-tunnel noise, it raises the issue of the effects of unsteady, or dynamic, effects on transition. These are also of interest because they can arise both due to the reflecting surface changing incidence resulting from steady body motion over a surface of variable slope, or due to changes in angle of incidence of the body itself. In this study, a moving-body numerical scheme was used to study the transition between regular and Mach shock wave reflections on a plane surface in steady supersonic flows under different rates of body incidence change. A wedge in a steady supersonic flow was used to generate an oblique shock wave that was reflected off of an ideal boundary