The flow in 2D channels of variable cross-section was studied numerically. The channels contain bodies that split the channels into narrow ones. Solutions of Euler's equations are obtained using the finite-volume solver of the Ansys CFX software package. A set of solutions is found. These solutions depend on the input Mach number and on the initial condition. Numerical simulations show a significant hysteresis in the drag coefficient of bodies in the channel relative to the supersonic Mach number set at the inlet. In a certain range of the inlet Mach number, there are asymmetric solutions of the equations.