The long-range energy deposition by heavy-ion beams makes new shock wave experiments possible in the laboratory. We have investigated a situation that is of relevance to supernova dynamics in astrophysics, where a shock wave is irradiated by a flux of neutrinos depositing energy throughout the shock wave and surrounding matter, thus changing the behavior of the running shock. We have carried out fluid-dynamical simulations to study generic features of stimulated shock waves. First we consider an idealized case assuming uniform energy deposition into a planar shock wave propagating through an ideal gas. Then we investigate more realistic situations realizable in laboratory experiments with heavy-ion beams. We have found that energy deposition leads to two important effects: acceleration of the shock front and decay of the shock strength. The possibility of laboratory experiments is briefly discussed.