This research aims to provide a useful algorithm for the prediction of the geometrical expansion of flat rings in the radialaxial ring rolling process in case of multiple variations of the mandrel feeding speed during the process. The proposed algorithm was subjected to a 2-phases validation process, where results were compared with those of laboratory experiments, conducted at 150℃ on rings made of AA-1070 and AA-6061 aluminum alloys, and with numerical simulations, considering 7 different rings with outer diameter ranging from 800 to 2000 ㎜ and made of 42CrMo4 steel alloy, Ti6Al4V titanium alloy and AA-6061 aluminum alloys. In the first and second validation phases, the maximum deviation in the estimation of the outer diameter of the ring has been calculated in 1.7% and 6.82%, respectively. According to the results of the validation, the proposed algorithm is able to properly predict the geometrical expansion of the ring for multiple variations of the mandrel feeding speed during the process and has good accordance with both relatively small and large rings.