The thread geometry and location of the contact points are the first steps in any study involving forces in the roller screw, yet most of the current literature makes restrictive assumptions and proposes methods which cannot be applied in the general case. The influence of profile shapes was only studied for standard roller screws and no method exists for the inverted type. Moreover, published general methods lack detail and can appear tough to apply from an engineering, practical point of view. In this paper, we propose an original model for the mechanism’s geometry which satisfies a double purpose: first, it is applicable to both standard and inverted roller screws and second, it is fast to compute and easy to implement. The shapes of our profiles are different from existing models and they are defined in the normal plane, which is more representative of the machine tool's point of view. All solids are assumed to be infinitely rigid. The proposed solution takes axial backlash into account and was optimized using a Newton-Raphson algorithm to provide results instantly. Finally, the model is compared with literature and we show how it can be used in the roller screw design process.