This thesis investigates the modeling and control of bio-inspired flexible structures for robotics applications. Many animals move through complicated natural environments and perform complex tasks by exploiting soft structures. Soft structures are highly versatile and are a growing area of interest in robotics because they can have decreased weight, size, and mechanical complexity relative to more traditional rigid robotics. This work uses planar discrete elastic rod (PDER) theory for modeling two types of flexible structures. First, a flexible airfoil is modeled using PDER theory, including the Improved Lighthill model (ILM) of hydrodynamic forces to study the propulsion thrust. The propulsion thrust generated by rigid and flexible foils are also measured experimentally and compared to the model. Second, a state-space description of a flexible pendulum with torque input is presented. Linear state-and output-feedback hybrid controllers stabilize the inverted flexible pendulum starting from the down equilibrium.