Abstract A new precision finishing process called magnetorheological abrasive flow finishing (MRAFF), which is basically a combination of abrasive flow machining (AFM) and magnetorheological finishing (MRF), has been developed for nano-finishing of parts even with complicated geometry for a wide range of industrial applications. This paper deals with the theoretical investigations into the mechanism of MRAFF process to study the effects of various process parameters. In the present work, an attempt has been made to analyze the medium flow through the fixture by finite difference method by assuming the medium as Bingham plastic to evaluate the stresses developed during the process. A capillary viscometer has been designed and fabricated to study the effect of magnetic field on the rheological properties of the medium. Microstructure of the mixture of ferromagnetic and abrasive particles in magnetorheological polishing fluid (MRPF) has been proposed, and normal force on the abrasive particles is calculated from the applied magnetic field. A model for the prediction of material removal and surface roughness has also been presented. Theoretical results compare well with the experimental data available in the literature.