Multiconic surfaces are a generalization of the type of surface called polyconic in numerical control of machine tools. The general theory is developed in this paper using a new parametrization. In the original form there was a problem as to whether or not a point that satisfies surface equations actually belonged to the intended surface. This difficulty is removed by the new technique. Algorithms for calculation of line and plane intersections with the surface and for calculation of normal vectors, volume, and surface area are given for classes of defining functions of which it is required only that they have appropriate conditions of continuity and differentiability. Examples are given of surfaces developed using spline functions. Preliminary comparative estimates of design and numerical control processing times are included.