In this study, a mathematical model for the prediction of the temperature evolution in the ring during the radial-axial ring rolling process is developed and used, together with the authors’ previous results, to determine analytically the flow stress of the material during process. These results, combined with Hill's slip-line field solution adapted to the RARR process, allow a fast and reasonably precise calculation of the radial forming force, a key parameter at the preliminary stage of the process design. The approach is validated by applying the proposed model to a case available in the literature and comparing the analytical results with those of the laboratory experiment and FEM simulation. Following the successful comparison, the models were applied to a large variety of flat rings, comparing analytical predictions with the results of FEM simulations. The accuracy of the analytical calculation and the reliability of the proposed models, for different ring configuration and process parameters, are presented and discussed.