The well‐known practice of using the mirror‐image, in theP, uplane, of the shock Hugoniot curve about a vertical line through the shocked statePH, uHis shown to give a complete thermodynamic description of metals when theU(shock velocity) vsuHrelationship and &agr;≡V‐1(&dgr;V/&dgr;T)P≈0are known. Use of the experimental relationshipU=c0+auH(aandc0constants) and &agr; = constant, leads to a thermodynamic description which results in the metal appearing less compressible than if described by the Mie—Gru¨neisen equation of state. Furthermore, the existance of an anomalous behavior ofcpin the low pressure neighborhood (<10 to <50 kbar depending on the metal) of the initial state rules out thesimultaneousexistence of a Hugoniot satisfying the linearUvsuHrelationship, of isentropes satisfying the mirror‐image assumption, and of a constant value of &agr; in this neighborhood. Thermodynamic functions for 16 metals are calculated up to 2 Mbars and compared with the results obtained from the Mie—Gru¨neisen equation of state.