We find that C-shocks propagating in molecular clouds can sputter the refractory materials which comprise the cores of interstellar grains. It is possible that the grains are completely destroyed at shock velocities of only 50 km s^-1. The rate of momentum transfer between the ionized and neutral fluids regulates the shock profile. Attention is paid to the dependence of the rate coefficient for the elastic scattering of ions and neutrals on their velocity difference. The intensities of infrared lines emitted by the shock are computed.