Hypersonic viscous ows near simple-shape bodies (wedge, cone, disk, and plate) have been studied numerically under the conditions of wind-tunnel experiments with underexpanded jets. The direct simulation Monte Carlo technique has been used to study the in uence of similarity parameters on the ow structure near the bodies and on the aerodynamic coef cients in hypersonic streams of air, nitrogen, helium, and argon. It has been found that, for conditions approaching the hypersonic stabilization limit, the Reynolds number and temperature factor are primary similarity parameters. The in uence of other parameters (speci c heat ratio, viscosity-approximation parameter, and the Mach number) becomes signi cant at low Reynolds numbers (less than 10) and small values of the hypersonic similarity parameter (less than 1). The numerical results are in good agreement with experimental data, which were obtained in a vacuum chamber at low and moderate Reynolds numbers from 0.1 to 200. In the studies of the pitching moment and lift coef cients, a three-dimensional numerical approach should be used to simulate nonuniform ow near a plate, cone, and wedge under the experimental conditions with freejets.