The exact flow behind a yawed conical shock wave is investigated. A numerical method of solving the differential equations of motion behind the shock wave is evolved. This method is applied to the case of the flow of a perfect gas behind a conical shock of semi-apex angle 30 degrees yawed at 20 degrees to a free stream of Mach number 10. The shape of the body which would produce such a shock wave is determined. The properties of the flow between the shock wave and the body surface are investigated particularly with respect to the variation of entropy and the streamline pattern. The existence of a singular generator on the body surface in the plane of yaw and on the "leeward" side, at which the entropy is many-valued is brought out. It is found that, downstream of the shock, all stream lines curve round and tend to converge to this singular generator. The body obtained by the present investigation is compared to the yawed circular cone which according to Stone’s first order theory would produce the same shock wave dealt with in this particular case.