Magnetorheological (MR) fluid is used as the working medium in MR finishing. The viscosity of the MR fluid, which determines the shear acting on the workpiece surface stress, can be controlled by the intensity of the applied external magnetic field, and is thus an important design parameter in the finishing process. Most previous studies have used a shear stress value obtained experimentally under a limited set of conditions. Although a recent theoretical model that predicts the shear stress in an external vertical magnetic field has been developed, it treats the energy variation with respect to the strain and the intensity of the magnetic field only among the adjoining particles in a chain. Because that model assumes no multi particle interactions, it is not well suited to a case in which the magnetic field is more than one dimension such as in MR finishing. In this study, a new three-dimensional model is proposed by expanding the one-dimensional model and considering multi particle interactions. The proposed model assumes that each particle is surrounded by the 26 neighboring particles, and the total internal energy is estimated by calculating the magnetic dipole interactions among the particles. Therefore, the proposed model considers not only the particle-to-particle energy variations, but also the chain-to-chain energy variations, The behavior of MR fluid is evaluated using the proposed model in a two-dimensional skewed magnetic field.