Abstract: Many aquatic animals propel themselves efficiently through water by oscillating flexible fins. These fins are, however, not homogeneously flexible, but instead their flexural stiffness varies along their chord and span. Here, we developed a low order model of these functionally-graded materials where the chordwise flexibility of the foil is modeled by one or two torsional springs along the chordline. The torsional spring structural model is then strongly coupled to a boundary element fluid model to simulate the fluid-structure interactions. We show that the effective flexibility of the combined fluid-structure system scales with the ratio of the added mass forces acting on the passive portion of the foil and the elastic forces defined by the torsional spring hinge. We further detail the dependency of the propulsive performance on the flexibility and location of the single torsional spring for a foil that is actively pitching about its leading edge. Our results show that increasing the flexion ratio by moving the spring away from the leading edge leads to enhanced propulsive efficiency, but compromises the thrust production. Proper combination of two flexible hinges, however, can result in a gain in both the thrust production and propulsive efficiency.