A time-dependent numerical method for calculating supersonic flow about blunt bodies at large angles of attack is presented. The axisymmetric bodies with sharp shoulders which are treated are constructed with a generator composed of segments of constant curvature. The nonaxisymmetric bodies have continuous slope and curvature. All flow fields are inviscid and adiabatic and have one plane of symmetry. A modification to the method of characteristics is introduced for use at the shock wave. A two-step finite-difference method of second-order accuracy is used at the body surface and in the region between the shock and body. A new finite-difference technique is introduced for use at sharp sonic shoulders. Comparisons of the results of the present method with experiment and the results of other methods are made for the flow of equilibrium air past the Apollo command module at the trim angle of attack and for perfect gas flow past a spherical cap and a spherically blunted cone at angle of attack. Both the cap and the blunted cone are terminated with sharp shoulders. Results are presented also for perfect gas flow past a prolate spheroid with its major axis normal to the flow.