This paper presents a numerical approach for the prediction of thrust generated by a fish-type biomimetic propulsion system. We model the fish as a non-uniform Timoshenko Beam (TB) with varying Young’s modulus and moment of inertia along its length from head to tail. The non-uniform Timoshenko beam is assumed to be a cantilever with the fixed end at the head and free end at the tail and the corresponding mode shapes are determined. Based on the mode shapes, the thrust is calculated with respect to the input parameters such as wave velocity, propulsive velocity and wavelength. The method developed here is shown to be useful for the design of bio-inspired propulsive systems for marine vehicles and also for gaining a better understanding propulsive mechanics of a robotic fish. In results, the thrust delivered by the simple flapping beam is identified and the relationship between the non-dimensional frequencies is determined. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.