Recent studies indicate that nature-inspired thrusters based on flexible oscillating foils show enhanced propulsive performance. However, understanding the underlying physics of the fluid–structure interaction (FSI) is essential to improve the efficiency of existing devices and pave the way for novel energy-efficient marine thrusters. In the present work, we investigate the effect of chord-wise flexibility on the propulsive performance of flapping-foil thrusters. For this purpose, a numerical method has been developed to simulate the time-dependent structural response of the flexible foil that undergoes prescribed large general motions. The fluid flow model is based on potential theory, whereas the elastic response of the foil is approximated by means of the classical Kirchhoff–Love theory for thin plates under cylindrical bending. The fully coupled FSI problem is treated numerically with a non-linear BEM–FEM scheme. The validity of the proposed scheme is established through comparisons against existing works. The performance of the flapping-foil thrusters over a range of design parameters, including flexural rigidity, Strouhal number, heaving and pitching amplitudes is also studied. The results show a propulsive efficiency enhancement of up to 6% for such systems with moderate loss in thrust, compared to rigid foils. Finally, the present model after enhancement could serve as a useful tool in the design, assessment and control of flexible biomimetic flapping-foil thrusters.