A model that considers the mutual interaction between particles and the external field in a magnetorheological (MR) fluid is proposed. The model predicts the magnetization, interaction energy density, and shear stress against an imposed strain along the planar direction under a uniform magnetic field. Using the Lekner summation method, slowly convergent magnetization functions are transformed into rapidly convergent ones. By applying the proposed model to an application suitable for commercial clutches and dampers working in direct shear mode, it is revealed that the mean magnetization vector and the associated functional quantities of the MR fluid behave harmonically with respect to the imposed shear strain.