A kinetic study including dissolution process and diffusion of the dissolved molecules for a stressed solid in contact with its solution is analyzed. We estimate a condition fixing the prevailing dissipation mechanism and analyze it with a linear stability criterion. This criterion depends on which process is limiting the rate of dissipation: dissolution at the solid-liquid interface or diffusion in the fluid. For definiteness we focus on recent experiments on various salts, which have shown that grooves, oriented perpendicular to the main compressive stress, develop on the free surfaces of crystals. We provide the characteristic length scale and the time scale for the development of this stress-induced roughening of solid surfaces, which are consistent with the experiments. Finally, we estimate these parameters for relevant geological conditions.