Abstract: A new method for the design of waverider configurations with more general shock geometries than previously possible is presented. An arbitrary, three-dimensional shock shape is specified as input, and a new inverse method, utilizing a cross-stream marching scheme for solving the Euler equations, is used to generate the post-shock flowfield. Unlike most previous studies, this approach allows for the use of nonaxisymmetric shock topologies with nonconstant shock strengths. The problem's ill-posedness is suppressed by reformulating the problem in the proper curvilinear coordinate system. The inverse marching approach is briefly summarized, and details of the waverider design procedure are given. Comparisons of individual waveriders and their flowfields generated by the new algorithm in a few seconds on a workstation with flowfields computed by the F3D Euler solver, requiring the order of an hour of Cray 2 CPU time, demonstrate the accuracy and efficiency of the new approach.