- Strong shock waves (SSW) propagating in a cold condensed matter and creating a dense plasma behind them are important for a wide variety of fields ranging from astrophysics to ICF. For high post-shock pressures, the electron contribution to the thermodynamic properties that are responsible for the stability of SSW is significant. In the present work, an analysis of two-dimensional instability of SSW in metals with respect to spontaneous acoustic emission has been performed. Such an instability may result in rippled shocks and, thus, in limitations on the efficiency of target implosion. An empirical Hugoniot adiabatic that represents a linear relation between the shock velocity D and the flow velocity U behind the shock was assumed. To calculate the criteria for spontaneous emission of sound, an equation of state is employed that is appropriate in the range of the post-shock temperatures that are of order or higher than the Fermi temperature. It was found that for various metals characterized by various values of the slope S= dD/dU of the Hugoniot adiabatic, the presence of free electrons increases the threshold for spontaneous emission but cannot eliminate it.