The endpoint stiffness, i.e., stiffness displayed by the wrist amid perturbations to the arm, has been used to assess the mechanical stability of the arm posture. The aim of this study is to develop an algorithm to optimally realize a desired end-point stiffness by minimizing muscle forces. The neuro-muscular behavior of the human arm during posture maintenance tasks is approximated by a two-link eight-muscle arm model. The model parameters reflect physiological data taken from published literature. The endpoint stiffness is shown to be a linear function of muscle activations. It is shown that the problem to minimize muscle activations while satisfying torque constraint at the joints can be solved by using non-negative least-squares method. Alternatively, linear programming can be used for this purpose. The biomechanical model is used to demonstrate how endpoint stiffness of desired magnitude, orientation, and eccentricity can be synthesized by activating arm muscles with minimal energy expenditure. Our simulation results suggest that bi-articular muscles play a major role in developing the desired endpoint stiffness. The model can be scaled up to three-dimensions by adding muscle groups.