The VEHICLE WITH TRAVELING WAVE THRUST MODULE 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. The fin, fin actuator or actuators, power source and central controller may be incorporated into a thrust module. Two thrust modules couple to each other via roll actuators and flexible coupling members may form a vehicle with exceptional maneuverability.