AbstractThe mathematical model of barotropic gas flow based on the two-layer flow representation with the regions of supersonic core and near-wall boundary layer is applied to the description of shock-wave structures in channels and nozzles of variable cross-section. The unsteady pseudoshock model is written in the form of the system of five inhomogeneous conservation laws. The disturbance propagation velocities are determined and the sufficient conditions of the hyperbolicity of the equations of motion are formulated. The formation of quasistationary shock waves and pseudoshock front oscillations is simulated numerically in the cases of periodic injection or variations in the channel exit section. The model is verified by means of the comparison with the available experimental data on forced pseudoshock oscillations in a transonic channel.