The linear shock-velocity (Us), particle-velocity (up) relation, which is known to be exceptionally successful in describing a wide variety of Hugoniot equation of state measurements, is shown to be virtually indistinguishable from the Birch-Murnaghan (third-order Eulerian finite strain) equation of state. For typical values of zero-pressure parameters, specially for the pressure derivative of the adiabatic bulk modulus K0S≂3 to 6, the Gr¿neisen parameter &ggr;0≂1.5 (¿1.0), and the logarithmic volume derivative of the Gr¿neisen parameter q≂1.0 (¿1.0), the Eulerian finite strain formulation yields the appropriate compressional moduli at infinitesimal strains, and it closely reproduces the Hugoniot at large compressions when compared with the linear Us-up relation. Thus shock wave measurements provide strong empirical support for the success of the Eulerian finite strain equation of state in describing the compression of condensed matter to high pressures. ¿ American Geophysical Union 1989