Adaptation of functions and mechanisms of biological systems can lead to new and innovative designs in a variety of energy conversion and propulsion systems. The present research aims at designing biologically-inspired and optimized energy harvesting and propulsive kinematics for aero- or hydro-foils, blades, and propellers with active and/or passive deformation. The computational methodology combines a mass-conserving immersed-boundary method, which is capable of simulating flow over non-grid-conforming complex moving bodies and a structural dynamics method, which is based on a finite-element method and is capable of predicting time-accurate linear and non-linear dynamics of composite structures. The pressure and velocity of fluid and geometric information of submerged structures are timeaccurately coupled through an integration algorithm. The high-fidelity simulation capability for prediction of fluidstructure interaction, is employed to achieve the goal of developing biologically-inspired novel kinematics of a flexible foil.