Ac conductivity measurements of marble samples have been carried out in the frequency range of 50kHz to 1MHz. Variations of frequency dependent conductivity were studied when the samples had previously suffered uniaxial compressional stress of various magnitudes up to fracture. The conductivity plots that were fitted by using the law σ = Α· fn indicated significant dependence of the exponent n on the previously suffered uniaxial compressional stress when the applied stress reached values where the material in terms of mechanical behaviour, shows a deviation from linear elasticity and microcracking occurs. A linear relation between variable v, which describes the variation of exponent n, and the damage variable D of the samples is evident.