Magnetorheological (MR) fluid is used for various applications due to its controllable viscosity. To predict the behavior of MR fluid under certain three-dimensional (3D) magnetic and shear strain fields, it is essential to model the fluid in an appropriate manner. The behavioral models used in the previous research, however, have serious limitations because most of them oversimplify the inter-particle interactions and employ assumptions valid only under specific geometric configurations and field conditions. In this study, a new model that can predict the behavior of MR fluid under arbitrary 3D magnetic and shear strain fields is proposed. The present work considers an MR fluid configured as a 3D infinite lattice structure. Using the proposed model, the shear stress components themselves, not the dipolar interaction energy, are calculated directly to avoid the mathematical singularity otherwise encountered. The resulting stress functions of the proposed model are transformed into rapidly convergent functions using the Lekner summation method. Finally, the characteristics of the stiffened MR fluid under a magnetic field are investigated using the transformed functions. Numerical computations on the original and transformed functions are performed and compared under selected conditions to ensure the validity and prove the high convergence efficiency of the proposed model.