This report presents a new method to find shapes that attain minimum wave drag under certain constraints. The constraints considered here are given values for the base area and the lift. The configuration is assumed to be embedded in a volume enclosed by two opposing circular Mach cones, one going through the most forward point of the configuration, the other through the rim of the base. The flow field inside this volume is entirely governed by the perturbation velocities on the Mach cone through the base. In fact, the method deals with the procedure to determine the value of these velocities. Once the velocity distribution along the Mach cone is known the flow field and thus the shape of possible configurations can be found by applying characteristic methods. Two cases are considered; in the first only the value of the base area is prescribed, while in the second also the lift is given. As an example the shape and the axis inclinations of a possible ring-wing configuration are calculated. The analysis is based on linearized supersonic flow theory. However, the method can also be adapted to non-linear flows around shapes with circular cross-sections.