This paper addresses turbulent 2D airflow in a simple intake model. The numerical simulation is based on the system of Reynolds-averaged Navier–Stokes equations. Numerical solutions of the system are obtained with a finite-volume solver of second order accuracy on a fine computational mesh. The location of shock waves, across which flow parameters change abruptly, is analyzed at three supersonic inflow Mach numbers in a band of back pressure given at the exit of intake. The obtained solutions show the occurrence of non-uniqueness and self-excited oscillations. Transitions between different flow regimes are discussed. A comparison with experimental data available in the literature is made.