In this paper slender-body theory is applied to flexible bodies. The bodies are assumed to have a constant forward velocity normal to the crests of a regular train of two-dimensional waves and to move at a nearly constant depth. A flexible recoil mode is defined which is the dynamic counterpart of the stretched straight fish position defined by Lighthill (1960) for uniform flow conditions. Expressions are derived for the mean thrust and for the mean rate of working, and permit the evaluation of conditions for efficient propulsion. By properly adapting the motions of the body to the oncoming waves, energy can be extracted from the waves in such a way that it can be used for propulsion. This phenomenon may help to explain the high speeds that cetacea are observed to sustain over long periods of time.