Turbulent airflow in a supersonic intake model of rectangular cross-section is studied numerically. Instability of shock waves formed in the intake and ahead of the entrance is examined. Solutions of the Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver of second-order accuracy. The expulsion and the swallowing of the shocks with a variation of free-stream parameters are studied at both subsonic and supersonic conditions prescribed at the outlet. Hysteresis in the dependence of 2D flow on the free-stream velocity and angle-of-attack is documented. An influence of 3D effects on the flow is examined.