Group Theoretical Methods as defined by Lie are applied to the problem of temperature independent, hydrodynamic shock in a Birch-Murnaghan continuum. Ratios of the group parameters are shown to be linked to physical parameters specified in the second, third, and fourth order BM-EOS approximations. We provide an illustrative example of how the expansion ratio(c1/c2)and the material resistance condition(c4/c2)are a function of the compression ratio &bgr;, for a spherical shock wave propagating through MgO and Na. ©2000 American Institute of Physics.