The paper presents the results of calculations of a supersonic laminar flow past a cylindrical body located between parallel horizontal walls (plates). The free-stream Mach number M = 5. Calculations were carried out for various values of the geometric factor χ defined as the ratio of the distance between the walls to the blunt diameter of the leading edge of the body, the ratio varying from 2 to infinity. Decreasing the distance between the walls was shown to lead to a shift of the separated shock closer to the streamlined body, and to an increase in the thickness of the separation region. In the case of χ = 2 a nonstationary self-oscillatory flow regime characterized by strong oscillations of the separated shock wave was realized.