The technique of Isothermal Depolarization Currents (IDC) was applied on marbles collected from Mt. Penteli (Greece) in order to investigate the influence of previously applied uniaxial compressional stress on IDC relaxation processes. The applied stress varied from early elastic range up to fracture. After each stress application IDC measurements were conducted and the relaxation parameters concerning fast and slow depolarization processes were studied. Experimental results manifest a differentiation in the shape of the depolarization current curves for the stressed and un-stressed samples. Specifically, during the final stage of the depolarization current decays faster when the geo-material has suffered stress adequate to cause microcracks in its structure, than the unstressed samples. Additionally, for severely damaged samples the initial stage of depolarization, dominated by "flip" transition mechanisms, lasts longer. It is concluded that the stress level influences "flip-flop" transition mechanisms that dominate the final depolarization stage and has no influence on "flip" transition mechanisms of the very initial stages of dipole rearrangement.