This paper investigates the role of chord-wise flexibility in the propulsive performance and the fluid structure interaction (FSI) dynamics of a flapping fin modelled as a chord-wise flexible cantilever beam with a sinusoidal support motion in an inviscid fluid. Finite element analyses and lumped vortex method have been employed to build the present FSI model. A comparative study of the average thrust coefficients has been carried out to optimize the chord-wise flexibility with respect to maximum thrust co-efficient achieved by the flapping fin. Moreover, the effect of the frequency of the support motion on the thrust coefficient has been looked into in this paper. It has been concluded that the increase in the chord-wise flexibility enhances the propulsive performance and the maximum value of thrust co-efficient is achieved when the flapping fin is actuated with the resonance frequency of the structure.