Actuation with variable elasticity is considered a key property for the realization of human-like bipedal locomotion. Also, an intelligent and self-stable mechanical system is indispensable. While much effort of current research has been devoted to the development of variable impedance joint actuators, this paper deals with the important question of how to determine the actuation requirements of a compliant, musculoskeletal robot that is targeted at fast dynamic motions. In a step-by-step approach, design decisions for the elastic humanoid robot BioBiped1 are presented. Using multibody system dynamics models and simulations, incorporating bidirectional series elastic actuator models and a realistic ground contact model, we analyze the actuation requirements of the employed electrical motors for computer generated hopping and human data based running motions. The numerical simulation results are accompanied by videos of the dynamics simulations. Recent experiments on the real hardware have indicated that the selected motor-gear units and elastic transmissions support the desired dynamic motion goals.