Studies of aquatic locomotion typically assume that organisms move through unbounded fluid. However, benthic fishes swim close to the substrate and will experience significant ground effects, which will be greatest for fishes with wide spans such as benthic batoids and flatfishes. Ground effects on fixed-wing flight are well understood, but these models are insufficient to describe the dynamic interactions between substrates and undulating, oscillating fish. Live fish alter their swimming behavior in ground effect, complicating comparisons of near-ground and freestream swimming performance. In this study, a simple, stingray-inspired physical model offers insights into ground effects on undulatory swimmers, contrasting the self-propelled swimming speed, power requirements, and hydrodynamics of fins swimming with fixed kinematics near and far from a solid boundary. Contrary to findings for gliding birds and other fixed-wing fliers, ground effect does not necessarily enhance the performance of undulating fins. Under most kinematic conditions, fins do not swim faster in ground effect, power requirements increase, and the cost of transport can increase by up to 10%. The influence of ground effect varies with kinematics, suggesting that benthic fish might modulate their swimming behavior to minimize locomotor penalties and incur benefits from swimming near a substrate.