In this paper, a new 5-axis tool positioning algorithm called the rotary contact method (RCM) for open concave surface machining using the toroidal cutter is developed. The RCM comes from the reverse thinking of multipoint machining (MPM) method and apparently distinguishes the traditional tool positioning principles, as it determines the optimal tool positions based on the offset surface instead of the design surface. The basic idea of the RCM is to determine the initial tool location first and then rotate the tool for required contact. The RCM can not only guarantee gouge-free tool positions without the additional local gouge checking and correction process but also effectively produce big machined strip width for open form surface machining just like the MPM. Besides, this new method is simple to implement. Machining simulation was performed to verify the validity of the RCM.