Inspired by the flexible wings and fins of flying and swimming animals, we investigate the flow induced by the interaction between a flapping flexible surface and the surrounding fluid for the limiting case of Strouhal number St ? 8 (zero free-stream speed). The model selected for this purpose is a two-dimensional sinusoidally pitching rigid symmetric foil to which is attached at the trailing edge a thin chordwise flexible surface (along the chord line). The flow so generated is a coherent jet aligned along the foil centreline, containing a reverse Bénard–Kármán vortex street and delivering a corresponding unidirectional thrust. We analyse the flow and thrust generation process. The measured velocity field suggests that the flow and thrust generation mainly occurs during the phases when the trailing edge is near the centreline. Flexibility of the surface is important in accelerating the near-wake flow and in transferring momentum and energy to the fluid. We present a detailed account of when and where the momentum and energy are added to the fluid. This study shows that the deformations of the flexible surface are responsible for generating a favourable pressure gradient along the jet direction, and for the observed unsteady actuator disc-type action. © 2018 The Author(s) Published by the Royal Society. All rights reserved.