Surface finish greatly affects the friction, wear, corrosion, heat transfer and lubrication properties of internal surfaces which find wide applications in medical, automobile, aerospace and mould and die industries. However, improving the internal surface finish is extremely challenging due to the restricted tool accessibility of conventional manufacturing processes. This paper develops a novel magnetic polishing tool to deterministically polish internal surfaces. Repeatability tests, single point polishing experiments and gap variation experiments are conducted to evaluate the performance of the proposed polishing tool. Experimental results substantiate the good repeatability and localized polishing capability with a material removal rate of 15 μm/min and achievable surface roughness of 0.258 μm Ra. Furthermore, a theoretical model is developed to reveal the material removal mechanism based on the contact mechanics model and sliding wear theory. The developed model can successfully predict the two-dimensional and three-dimensional polished profiles under different gaps which are defined by the distance between the externally driven magnet and the outer surface of the workpiece. The localized polishing capability is, for the first time, achieved in internal surface finishing and the theoretical study establishes a novel framework for modelling the polished profile evolution in pressure-copying polishing processes. Display omitted •Localized polishing capability is for the first time achieved in internal finishing.•Material removal rate reaches 15 μm/min and surface roughness improvement is 88%.•Gap is the dominant factor influencing material removal rate.•A material removal model is developed based on contact mechanics and wear theory.