The inverse magnetostrictive effect, also called magnetomechanical effect, in Terfenol-D material, has been investigated in this paper. Based on Stoner-Wohlfarth (SW) model, taking into account magnetocrystalline and stress-induced anisotropy energy, and following the free energy minimization procedure, direction cosines of magnetization in Terfenol-D single crystal in demagnetized state have been obtained as a function of the compressive stress. The nonlinear equations for equilibrium have been solved numerically. The results indicated that under compressive stress, magnetic anisotropy in Terfenol-D is determined by a competition between magnetocrystalline and stress-induced anisotropy energy, and changes from cubic symmetry to uniaxial. A comparison between experimental and numerical results showed that there is a maximum magnetostriction in Terfenol-D at a certain stress. According to our numerical results, experimental observations that compressive stress makes Terfenol-D hard to be magnetized and leads to the maximum magnetostriction can be explained. The computation in this paper presents a more accurate approach to similar investigations, and its numerical results would be helpful for a better understanding of magnetization process of similar materials.