Study of the ac conductivity is attempted on rock materials and specifically, marble samples collected from Mt. Penteli Attica. The ac conductivity measurements have been carried out in the frequency range of 50kHz to 1MHz. Consequent measurements were carried out on samples that had previously suffered uniaxial compressional stress of various magnitudes up to fracture. The conductivity plots were fitted by using a frequency power law. The power law exponent, n, indicated a significant dependence on the previously applied uniaxial compressional stress when the applied stress had reached values leading the material beyond the linear elasticity range and causing microcracking. Accordingly, after taking into account the stress-strain curves of the samples, the damage variable D was calculated and correlated to a corresponding variable k which characterizes the deviations of the frequency exponent n from its normal values i.e. when no destructive procedures have taken place in the samples. The experimental results indicated that the two variables are related linearly.