Reverse engineering of biological form and function requires hierarchical design over several orders of space and time. Recent advances in the mechanistic understanding of biosynthetic compound materials1,2,3, computer-aided design approaches in molecular synthetic biology4,5 and traditional soft robotics6,7, and increasing aptitude in generating structural and chemical microenvironments that promote cellular self-organization8,9,10 have enhanced the ability to recapitulate such hierarchical architecture in engineered biological systems. Here we combined these capabilities in a systematic design strategy to reverse engineer a muscular pump. We report the construction of a freely swimming jellyfish from chemically dissociated rat tissue and silicone polymer as a proof of concept. The constructs, termed 'medusoids', were designed with computer simulations and experiments to match key determinants of jellyfish propulsion and feeding performance by quantitatively mimicking structural design, stroke kinematics and animal-fluid interactions. The combination of the engineering design algorithm with quantitative benchmarks of physiological performance suggests that our strategy is broadly applicable to reverse engineering of muscular organs or simple life forms that pump to survive.