The goal of this work was to investigate stability in relation to the magnitude and direction of forces applied by the hand. The endpoint stiffness and joint stiffness of the arm were measured during a postural task in which subjects exerted up to 30% maximum voluntary force in each of four directions while controlling the position of the hand. All four coefficients of the joint stiffness matrix were found to vary linearly with both elbow and shoulder torque. This contrasts with the results of a previous study, which employed a force control task and concluded that the joint stiffness coefficients varied linearly with either shoulder or elbow torque but not both. Joint stiffness was transformed into endpoint stiffness to compare the effect on stability as endpoint force increased. When the joint stiffness coefficients were modeled as varying with the net torque at only one joint, as in the previous study, we found that hand position became unstable if endpoint force exceeded about 22 N in a specific direction. This did not occur when the joint stiffness coefficients were modeled as varying with the net torque at both joints, as in the present study. Rather, hand position became increasingly more stable as endpoint force increased for all directions of applied force. Our analysis suggests that co-contraction of biarticular muscles was primarily responsible for the increased stability. This clearly demonstrates how the central nervous system can selectively adapt the impedance of the arm in a specific direction to stabilize hand position when the force applied by the hand has a destabilizing effect in that direction.