Shock expansion theory was first used by Epstein to calculate the characteristics of aerofoils with sharp leading edges and attached shock waves. In this case the aerofoil characteristics were found by assuming that the flow downstream of the leading edge shock was the same as in a Prandtl-Meyer expansion with all reflected waves neglected. In 1955 Eggers and Savin considered the extension of the method to three-dimensional hypersonic flows, with particular reference to bodies of revolution at incidence. Eggers and Savin point out that the most important factor influencing the method is the accuracy of the basic conical solution at the apex, since inaccuracies at the apex are reflected strongly in the pressures downstream. For this reason most applications of the method have been restricted to inclined bodies of revolution with pointed noses, since solutions for yawed cones can be used to start the solutions. Recently it has been shown that thin-shock-layer theory as originally developed by Messiter can give accurate solutions for the shock shapes and pressure distributions on the lower surfaces of conical bodies with a wide variety of cross-section shapes and for a wide range of hypersonic flight conditions.