Body and caudal fin fish, like tuna and eels, are classified on a scale of kinematic modes from thuuniform to anguilliform. What differentiates the thuuniform and anguilliform motion is the relative dominance of standing and traveling waves in their body’s deformation. The anguilliform swimming mode, where a traveling wave is propagated along the body length, is desirable for certain applications of bio-inspired underwater vehicles because of its low-speed efficiency and high maneuverability. In nature, anguilli form swimmers are more flexible and slender than thuuniform fishes. The aim of this paper is to study the relationship between body flexibility, fluid damping, and induced swimming kinematics in a bio-inspired propulsor. A nonlinear electro-hydro-elastic model was derived and a parametric study was conducted over different body stiffness. To find the relative strength of standing and traveling waves in the body deformation the steady-state response was analyzed using orthogonal decomposition. Traveling wave quality was dependent on excitation frequency and the presence of nonlinear fluid damping. A peak in traveling wave quality was induced at the natural frequencies due to significant nonlinear fluid loading. At the first couple natural frequencies, flexible beams had greater overall traveling wave quality, but stiffer beams exhibited a stronger nonlinear response. While future work is needed to examine the high frequency response of flexible structures, the frequency band which maximizes traveling wave quality may identify an optimal regime for passively flexible bio-inspired propulsors.