In this paper, the author introduces shaping principle of machining non-sphere with rotary electrode, analyses in greater detail the functions of machining non-sphere system with rotary electrode and the motion laws of machining rotary work-pieces. On the basis of those works, the general laws of forming non-sphere through rotary tool electrode’s beveling circle are studied. The author establishes for the first time the universal mathematical models. This lays a foundation of mathematics for computer simulation, virtual machining and establishment of the real machining system of machining non-sphere by rotary electric discharge machining (EDM).