A series-elastic actuator (SEA) can provide remarkable performance benefits in a robotic system, allowing the execution of highly dynamic manuevers, such as a jump. While SEAs have been used in numerous robotic systems, no comprehensive understanding of an optimal design exists. This paper presents a new analytical basis for maximizing an SEA thrust performance for jumping from rest with an articulated leg. The analytical SEA model is validated with simulation and experimental results from a prototype leg. An SEA decouples the dynamic limitations of a dc motor actuator from the joint, allowing larger lift-off velocities than with a directly driven joint. A detailed analysis of the complex dynamic response of an SEA during the thrust phase leads to a new maximum impulse criterion, where motor speed is approximately half the no-load speed at the moment of peak motor torque. The analytical model and this proposed criterion are used to develop a simple equation for selecting SEA design parameters. Lastly, a novel unidirectional SEA design is presented that allows for accurate positioning of the leg during flight.