In today's world, the hemispherical-shaped component's fine finishing with high wear resistance and dimensional accuracy is required in different applications such as shells, molds, implants. The magnetorheological finishing (MRF) process with a novel hemispherical tip-based tool is used to finish the hemispherical cups. The study aims to develop a novel mathematical model theoretically for predicting the surface roughness reduction of the hemispherical shaped workpieces using the present MRF process. In the MRF process, the magnetic field controls the external forces, therefore, the magnetic flux density (MFD) effect on the fine finishing of the hemispherical shaped workpieces has been studied theoretically and further validated experimentally. Next, to validate the present mathematical model, experiments are done over the hemispherical shaped acetabular cups. The results of the predicted roughness match well with the experimental values with the error range from 1.17 % to 6.15 %. To analyze the efficacy of the present process, the surface morphology tests is performed on workpiece using scanning electron microscopy. The present mathematical model for the MRF process predicts fine finishing along with the overall enhancement in the surface quality of the hemispherical shaped cup surface.