Based on an optical or a gauge‐and‐optical method, shock Hugoniot curves for two kinds of polyethylene (PE) specimens, i.e., high‐density polyethylene (HDPE) and linear low‐density polyethylene (LLDPE), have been measured in the shock stress region up to 1 GPa. It is found that the shock‐versus‐particle velocity Hugoniot curves for these PE specimens are non‐linear in this shock stress region. As one of the reasons for this non‐linearity, it is plausible that the molecular chains of polymers have anharmonic potential in the direction of intermolecular motion and intramolecular motion. The Gru¨neisen parameter of representing the anharmonic properties of the potential has been calculated from the obtained Hugoniot curves for these PE specimens. Calculated values of the parameter change rapidly from large to small values with shock compression up to 1 GPa shock stress. Large values of the parameter correspond to the selective excitation of the intermolecular vibrational modes of with lower phonon frequency. It is revealed that the non‐linearity of the Hugoniot curves for the PE specimens results from the drastic increase of the number of the excited vibrational modes of intramolecular motion in case the value of shock stress exceeds some level. © 2004 American Institute of Physics