A water tunnel study of the effect of spanwise flexibility on the thrust, lift and propulsive efficiency of a rectangular wing oscillating in pure heave has been performed. The thrust and lift forces were measured with a force balance, and the flow field was measured with a Particle Image Velocimetry system. Introducing a degree of spanwise flexibility was found to be beneficial. For Strouhal numbers greater than 0.2, a degree of spanwise flexibility was found to yield a small increase in thrust coefficient, and a small decrease in power-input requirement, resulting in higher efficiency. In this case, a moderately stronger trailing-edge vortex system was observed. Introducing a far greater degree of spanwise flexibility, however, was found to be detrimental. A large phase delay of the wing tip displacement was observed, leading to the root and tip moving in opposite directions for a significant portion of the flapping stroke. Vorticity of opposing sign was observed to be shed from the root and tip, resulting in a weak and fragmented vorticity pattern. The thrust coefficient was observed to be significantly reduced, and the efficiency diminished. It is noted that the range of Strouhal numbers for which spanwise flexibility was found to offer benefits overlaps the range found in nature, of 0.2