Results of measurement of the Gruneisen coefficient of two anisotropic materials (4KMS carbon-carbon composite and UPV-1 pyrolytic carbon) are presented. The values of the Gruneisen coefficient are calculated on the basis of the measured amplitude of mechanical stresses arising in the material with absorption of electron-beam energy. The results for the 4KMS composite include not only a negative value of the Gruneisen coefficient in the range of electron energy density of several tens of joules per square centimeter but also its anomalously low value as compared to other materials. Significant decay of the stress wave propagating over this material is noted. The Gruneisen coefficient of the UPV-1 sample varies depending on the sample orientation.