Recent advancements in computational fluid dynamics have enabled researchers to efficiently explore problems that involve moving elastic boundaries immersed in fluids for problems such as cardiac fluid dynamics and animal swimming. These advances have also made modeling both nutrient exchange in a fluid and the muscle-driven motion of a flexible organ or organism through a fluid feasible. The work presented here focuses on the development and implementation of such methods and models for the pumping and pulsation of jellyfish bells used for swimming and feeding. We leverage existing computational algorithms for fluid-structure interactions and extend this technology to “living” boundaries. The models are used to reveal the role of resonance in jellyfish swimming and turning swimming and the effect of porous boundaries on particle capture.