Vessel having a non-planing hull provided with an attached foil which is below the surface of the water and spaced from the hull. The foil is attached in proximity to the aft end of the vessel, and is oriented with a downward tilt relative to the horizontal to provide a lifting force with a force component in the forward direction. The foil can be located entirely behind the vessel, partly below the aft hull portion of the vessel, or entirely therebelow. In the latter case, the hull is preferably provided with a recess.