This study thoroughly analyses the parameters affecting aerodynamic performance and the shapes of the multi-directional curvature waverider. This hypersonic vehicle is developed from a hypersonic flowfield of a perturbed cone with longitudinal and transverse curvatures, as derived by combining the hypersonic small disturbance theory (HSDT) with the perturbation method. A range both theoretically and practically sound is also determined to alter the parameters. Numerical methods are then used to find the vehicle's optimal shape having a maximum lift, lift–drag ratio, or volumetric ratio when the viscous effect is considered. Furthermore, the curve fitting method is utilized to establish a set of approximate equations capable of speedily estimating the aerodynamic performance and the volumetric ratio. In addition several samples are presented to illustrate how to use this set of equations to generate the optimal shape under any combination of constraints in the lift–drag ratio, lift, and volumetric ratio. Notably, the viscous effect is approximate and takes no account of displacement corrections. Moreover, the base drag is neglected here.