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Some anguilliform swimmers such as eels and lampreys swim near the ground, which has been hypothesized to have hydrodynamic benefits. To investigate whether swimming near ground has hydrodynamics benefits, two large-eddy simulations of a self-propelled anguilliform swimmer are carried out—one swimming far away from the ground (free swimming) and the other near the ground, that is, midline at 0.07 of fish length (L) from the ground creating a gap of 0.04 L . Simulations are carried out under similar conditions with both fish starting from rest in a quiescent flow and reaching steady swimming (constant average speed). The numerical results show that both swimmers have similar speed, power consumption, efficiency, and wake structure during steady swimming. This indicates that swimming near the ground with a gap larger than 0.04 L does not improve the swimming performance of anguilliform swimmers when there is no incoming flow, that is, the interaction of the wake with the ground does not improve swimming performance. When there is incoming flow, however, swimming near the ground may help because the flow has lower velocities near the ground.