Flexible joint has the most critical role in Thrust Vector Control (TVC) solid fuel rockets. In this paper, a new analytic method for calculation of stiffness of spherical Elastomer-Metal joint by the theory of linear elasticity and Velasof Kantorowicz analytic method is developed. Velasof Kantorowicz analytic method is based on cross displacement which is driven from bending equation. Then flexible joint is simulated by ABAQUS code under bending load when thrust vector angle is critical (i.e. 15 degrees). Seven different configurations of metal and rubber layers are considered. In each configuration, required bending is determined when thrust vector is 15 degrees and maximum stress is calculated. Based on these results best selection of elastomer material and stiffness is proposed. Finally, the results of analytical and those of simulation are compared which show good agreement. This comparison shows that the derived formula predicts stresses precisely.