People often complete tasks using one hand for the task and one hand for support. These one-handed support tasks can be found in many different types of jobs, such as automotive assembly jobs. Optimization-based posture prediction has proven to be a valid tool in predicting the postures necessary to complete the tasks, but the related external support forces have been prescribed and not predicted. This paper presents a method in which the optimal posture and related supporting hand forces can be predicted simultaneously using optimization and stability analysis techniques. Postures are evaluated using a physics-based human performance measure (HPM) while external forces are assessed using stability analysis. The physics-based performance measures are based on joint torque. Stability is analyzed using criteria based on a 3D zero moment point (ZMP). The human model used in the prediction contains 56 degrees of freedom and is based on a 50th percentile female in stature. Tasks based on common automotive assembly one-handed tasks found in literature are considered as examples to test the proposed method. Overall, the predicted supporting hand forces have good correlation with experimentally measured forces.