When a material is subjected to an alternating stress field, there are temperature fluctuations throughout its volume due to thermoelastic effects. The resulting irreversible heat conduction leads to entropy production which, in turn, is the cause of thermodynamic damping. An analytical investigation of the entropy produced during a vibration cycle due to the reciprocity of temperature rise and strain yielded the change of the material damping factor as a function of shape and magnitude of the porosity of the material. A homogeneous, isotropic, elastic bar of cylindrical shape is considered with uniformly distributed ellipsoidal cavities under alternating uniform axial stress. The analytical calculation of the dynamic characteristics of the porous structure yielded the change of the material damping factor as a function of shape and magnitude of the porosity of the material. A homogeneous, isotropic, elastic bar of cylindrical shape is considered with uniformly distributed ellipsoidal cavities under alternating uniform axial stress. The analytical calculation of the dynamic characteristics of the porous structure yielded the damping factor of the bar and the material damping factor. Experimental results on porous metals are in good correlation with analysis.