We study impacts of a rigid body on a thin elastic sheet floating on a liquid. When struck by a solid object of small size, the elastic sheet deforms and waves propagate in and on the membrane. The impact triggers a longitudinal elastic wave effectively stretching the membrane. The hydroelastic transverse wave that propagates in the stretched domain is similar to capillary waves on a free surface with an equivalent ‘surface tension’ that results from the stretching of the elastic membrane. Two limiting cases, for which a self-similar solution can be computed, corresponding to short and long times are identified. Surprisingly, our study reveals that the fluid–body system behaves as a regular liquid–gas interface, but with an effective surface tension coefficient that scales linearly with the impact velocity.