Bodies that absorb, reflect or generate wave energy are submitted to mean forces. For moving bodies the mean forces in the direction of motion contribute to the drag or propulsion of the body. For flexible and deformable slender bodies swimming in waves at a constant forward velocity U normal to the crests of the waves, the mean rate of working $\overline{W}$ and the mean thrust $\overline{T}$ are evaluated. When the waves are assumed to be not significantly affected by the swimming slender bodies it is found that the Froude efficiency of propulsion for cases without shedding of vorticity is invariably given by U/(U + c), U + c being the phase velocity of the waves with respect to the body. The result remains valid when shedding small amounts of vorticity. $\overline{T}$ is obtained as the result of the radiation stress, and is proportional to $\overline{W}$.

The same efficiency can be realized by two-dimensional bodies oscillating in regular trains of two-dimensional waves. It is also valid for wave-making boats. For three-dimensional cases U/(U + c) represents the upper limit when the outgoing waves are properly beamed. Actuator surfaces with constant loading will be interpreted as vortex wavemakers.