The function of many muscles during natural movements is to accelerate a mass. We used a simple model containing the essential elements of this functional system to investigate which musculoskeletal features are important for increasing the mechanical work done in a muscle-powered acceleration. The muscle model consisted of a muscle-like actuator with frog hindlimb muscle properties, operating across a lever to accelerate a load. We tested this model in configurations with and without a series elastic element and with and without a variable mechanical advantage. When total muscle shortening was held constant at 30%, the model produced the most work when the muscle operated with a series elastic element and an effective mechanical advantage that increased throughout the contraction (31 J kg(-1) muscle vs 26.6 J kg(-1) muscle for the non-compliant, constant mechanical advantage configuration). We also compared the model output with the dynamics of jumping bullfrogs, measured by high-speed video analysis, and the length changes of the plantaris muscle, measured by sonomicrometry. This comparison revealed that the length, force and power trajectory of the body of jumping frogs could be accurately replicated by a model of a fully active muscle operating against an inertial load, but only if the model muscle included a series elastic element. Sonomicrometer measurements of the plantaris muscle revealed an unusual, biphasic pattern of shortening, with high muscle velocities early and late in the contraction, separated by a period of slow contraction. The model muscle produced this pattern of shortening only when an elastic element was included. These results demonstrate that an elastic element can increase the work output in a muscle-powered acceleration. Elastic elements uncouple muscle fiber shortening velocity from body movement to allow the muscle fibers to operate at slower shortening velocities and higher force outputs. A variable muscle mechanical advantage improves the effectiveness of elastic energy storage and recovery by providing an inertial catch mechanism. These results can explain the high power outputs observed in jumping frogs. More generally, our model suggests how the function of non-muscular elements of the musculoskeletal system enhances performance in muscle-powered accelerations.