A method is developed which accurately predicts for blunt-based bodies of revolution the normal force coefficient and the pitching moment coefficient for angles of attack far beyond the range of potential theory. It is based on the principle of superposition of the results of potential theory and the viscous force on a cylindrical body due to the transverse component of flow. In contrast to previously used methods, the viscous cross force is assumed not to be in a steady state, but in a transient development along the body. The method is compared with experimental data for both subsonic and supersonic flows and with both laminar and turbulent axial boundary layers. The method is also useful for extrapolation of small-yaw data to large yaws and to different Reynolds numbers. The results presented have been applied only in the range M = 0 to M = 2.87 and for a limited range of Reynolds numbers.