The polarization produced by a shock wave has been measured for shock pressures up to 297 kbar in Plexiglas and 207 kbar in polystyrene. The polarization is produced at the shock front and undergoes relaxation after the front has passed. For both materials, Hugoniot data indicate a high‐pressure phase transition which is correlated with rapid changes in the dielectric properties of the shocked material. At the phase transition, the polarization produced at the shock front and the dielectric constant of the shocked material increase more rapidly, while the relaxation time suddenly decreases. The changes in dielectric properties at the phase transition suggest that the high‐pressure phase is more fluid.