A bionic jellyfish is a robot that can mimic the swimming of a real jellyfish. In practical application, the volume and the capacity of its carrying power are limited, hence its power consumption is a crucial factor for continuous swimming. The purpose of this paper is to propose an approach for the resonance analysis of bionic jellyfishes in order to investigate their energy efficiency in swimming. First, a suitable rigid-body bionic jellyfish was chosen from the previous study, and then its design approach was presented, Then, it was transformed into a compliant design, by the proposed method, in order to mimic the motion of a real jellyfish. Furthermore, its solid model was drawn, and the approach of modal analysis by using ANSYS software was addressed. After that, two terms, specific energy and energy ratio, were defined in order to evaluate its energy efficiency. Finally, a design example was given for illustration, and its motion simulations with and without resonance input were conducted by using ADAMS software. Additionally, their specific energies and energy ratios were found. The simulation results showed that the required input energy would be significantly reduced if a bionic jellyfish swims at its resonance frequency. bionic robot, jellyfish, compliant mechanism, resonance analysis Citation:Hsieh W H, Chen T I. On the resonance analysis for compliant bionic jellyfishes.