Different aspects of the transition between regular and Mach reflectio
ns of strong shock waves in steady flows are numerically studied. Two
approaches-kinetic (the direct simulation Monte Carlo method) and cont
inuum (Euler equations)-are used to investigate the hysteresis phenome
non in the flow about two symmetrical wedges in two- and three-dimensi
onal statements. The dependence of the final shock wave configuration
on initial conditions, the transition from regular to Mach reflection
by means of flow perturbations, and three-dimensional effects are exam
ined. The three-dimensionality of the flow is shown to increase the an
gles of transition from regular to Mach reflection and back and to dec
rease the Mach stem height.