The TRAVELING WAVE PROPELLER, PUMP AND GENERATOR APPARATUSES, METHODS AND SYSTEMS include force or forces applied to an arc-like flexible sheet-like material to create a deformed crenated strip fin with strained-deformations. The strained-deformations take on a sinusoid-like form that express the internal energy state of the flexible sheet-like material after it has been configured into a crenated strip fin. After being incorporated into a mechanism with couplings that prevent the crenated strip fin from returning to its un-strained state, the strained-deformations persist. Actuators may be used to sequentially rotate vertebrae attached to the fins causing the travel of sinusoid-like deformations along the fins. In a fluid medium, the traveling waves of sinusoidal deformations may exert force on the fluid causing the fluid to move and/or creating thrust. When anchored in moving fluid, hydrodynamic loading of the fins may cause the fins to move and transmit force to an electromagnetic generator or other energy-harnessing transducer to generate electricity.