Some mathematical model is proposed of a flow in a long channel with compliant walls. This model allows us to describe both stationary and nonstationary (self-oscillatory) regimes of motion. The model is based on a two-layer representation of the flow with mass exchange between the layers. Stationary solutions are constructed and their structure is under study. We perform the numerical simulation of various flow regimes in presence of a local change of the wall stiffness. In particular, the solutions are constructed that describe the formation of a monotonic pseudoshock and the development of nonstationary self-oscillations.