Messiter's thin shock layer approximation for hypersonic wings is applied to several non-conical shapes. Two calculation methods are considered. One gives the exact solution for a particular three-dimensional geometry which possesses a conical planform and also a conical distribution of thickness superimposed upon a surface cambered in the chordwise direction. Agreement with experiment is good for all cases, including that where the wing is yawed. The other method is a more general approach whereby the solution is expressed as a correction to an already known conical flow. Such a technique is applicable to conical planforms with either attached or detached shocks but only to the non-conical planform for the region in the vicinity of the leading edge when the shock is attached.