The technique of Dielectric Spectroscopy (DS) or Impedance Spectroscopy (IS) was applied on marbles in order to investigate the influence of previously applied uniaxial compressional stress and three point bending up to fracture. Parameters to be measured were the ac conductivity (σac), the real (ε΄) and the imaginary (ε΄΄) parts of complex relative permittivity when an ac electric field at frequencies 10kHz and 100kHz was applied upon dry and saturated samples which were successively subjected to higher levels of mechanical stress. The experimental results indicate that there are systematic declinations in the values of the above parameters between the state of stress and the state of relaxation. These declinations become more intense at higher stress values. It is concluded that the technique of dielectric spectroscopy constitutes a promising method of investigation and quantification of the damage that has occurred within the bulk of geomaterials.