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A thermodynamic description of metals in the range of high pressures and temperatures is obtained and applied to the problem of the stability of strong shock waves under spontaneous emission of sound. A three-term form of the equation of state is employed to describe the contributions of the cold elastic pressure, the thermal atomic pressure, and the thermal pressure of the free electrons to the total pressure. The full determination of the equation of state is performed from the experimental Hugoniot data and from a model (such as the Slater–Landau model) connecting the atomic Grüneisen parameter and the atomic cold pressure. From the equation of state, the behavior of the Mach number, the temperature, and the entropy along the Hugoniot adiabatic is obtained and analyzed. The calculation of the sound velocity behind the shock enables the application of the Kontorovich criterion for the spontaneous emission of sound from the shock’s front. It is shown that metals with a relatively low slope of the shock velocity versus the particle-velocity straight line exhibit such an unstable behavior for high enough shock intensities. The effects of the electrons’ thermal pressure on both the thermodynamic properties of the metals and the stability of shocks are analyzed and discussed. In particular, it is shown that the electronic contribution to the total pressure has a stabilizing effect. © 1997 American Institute of Physics.