Studies of dielectric relaxation and ac conductivity of marble samples collected from Mt. Penteli (Attica) have been carried out in the frequency range of 150Hz to 1MHz. Initially reference measurements were conducted under atmospheric pressure for all of the samples. Subsequently the samples were subjected to various compressive stresses of approximately 300s duration each. Then, the stress was removed and dielectric constant and loss measurements were conducted. The experimental results indicate a large permanent differentiation a long relaxation time if the applied stresses are beyond the elasticity limit and the material is stressed in the plastic region.