Many tasks require the arm to move from its initial position to a specified target position, but leave us free to choose the trajectory between them. This paper presents and tests the hypothesis that trajectories are chosen to minimize metabolic energy costs. Costs are calculated for the range of possible trajectories, for movements between the end points used in previously published experiments. Calculated energy minimizing trajectories for a model with biarticular elbow muscles agree well with observed trajectories for fast movements. Good agreement is also obtained for slow movements if they are assumed to be performed by slower muscles. A model in which all muscles are uniarticular is less successful in predicting observed trajectories. The effects of loads and of reversing the direction of movement are investigated.