We present experimental evidence for the hydrodynamic benefits of swimming 'in ground effect', that is, near a solid boundary. This situation is common to fish that swim near the substrate, especially those that are dorsoventrally compressed, such as batoids and flatfishes. To investigate flexible propulsors in ground effect, we conduct force measurements and particle image velocimetry on flexible rectangular panels actuated at their leading edge near the wall of a water channel. For a given actuation mode, the panels swim faster near the channel wall while maintaining the same propulsive economy. In conditions producing net thrust, panels produce more thrust near the ground. When operating in resonance, swimming near the ground can also increase propulsive efficiency. Finally, the ground can act to suppress three-dimensional modes, thereby increasing thrust and propulsive efficiency. The planform considered here is non-biological, but the hydrodynamic benefits are likely to apply to more complex geometries, especially those where broad flexible propulsors are involved such as fish bodies and fins. Such fish could produce more thrust by swimming near the ground, and in some cases do so more efficiently.