The turbulent airflow in 2D and 3D channels with bends of opposite walls is studied numerically. The channels are slightly divergent in the longitudinal direction upstream and downstream of the bends. The flow is supersonic on the inlet and outlet boundaries of the computational domain. Solutions of the Reynolds-averaged Navier–Stokes equations are obtained with a finite-volume solver of second-order accuracy. The solutions demonstrate considerable hysteresis under variations of the free-stream Mach number or angle of attack. At the ends of hysteresis bands, the flow structure changes drastically due to instability of shock wave positions. Effects of 3D phenomena, turbulent viscosity, and thickness of walls on the hysteresis are discussed.