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This paper investigates the role of chord-wise flexibility in propulsive performance and the fluid structure interaction (FSI) coupled with FEM dynamics of a flapping fin in a viscid fluid. Inviscid environment limits the deflections of the plate elements and separation is inevitable in the case of large deformations. Hence we propose to use N-S solver coupled with FEM solver to emphasize the limit of applicability of the aerodynamic theory. Moreover, inclusion of the viscous effects can potentially result in interesting dynamical behaviour. A comparative study of the thrust coefficients achieved by the flapping fin has been carried out in this paper. It has concluded that increase in the chord-wise flexibility enhances the propulsive performance and maximum value of thrust coefficient.