In this paper, we use multiscale modeling to explore the coupling of the atomic orbital and magnetic moment and their evolutions under the excitations of external stress and magnetic fields. Our results of density functional theory (DFT) calculations show that strain-induced spin reorientation and redistribution of orbital coupling are the fundamental reasons for altering the atomic magnetic moment, magnetic anisotropy, and exchange interactions. Also, magnetic anisotropy and exchange interactions are found to play a more crucial role in the magnetization reversal process than the atomic magnetic moment. By using micromagnetics approach and the finite element method (FEM), the macroscopic magnetic properties such as coercivity, magnetic permeability, and remanence alter as a consequence of modified electronic structure, which eventually leads to the distortion of the macroscopic magnetic field of the stress concentration area. Through DFT, micromagnetics and FEM approaches, the cross-scale simulations herein highlight the remarkable short-range orbital ordering and coupling in ferromagnetic materials which provide the fresh insight in the stress-magnetic coupling for MMM applications.