Based on the observation that the boundary surface of a rotary milling cutter can be represented as the envelope of a one-parameter family of spheres, the analytical expression of the surface swept by a milling cutter undergoing a general spatial motion is derived in a very simple way by using the envelope theory of two-parameter family of spheres. For a toroidal cutter, two methods for determining the effective patch of the obtained envelope surface are proposed. The results can be applied to multi-axis numerical control machining simulation and verification, tool collision check, accuracy evaluation, row spacing optimization and tool path generation. The simulation results show that the proposed method has high precision and high stability.