To better describe the damping behavior of rock, a new method was developed to calculate damping parameters in consideration of lateral and longitudinal damped vibrations. A series of damping experiments was also conducted on sandstone, conglomerate and glutenite under dynamic cyclic loading, the stepped cyclic loading and the constant amplitude cyclic loading, respectively. Then response characteristics of damping parameter to stress amplitude and strain amplitude were both obtained. This study revealed the evolution laws of the damping ratio and the damping coefficient with the cycle number under the constant amplitude cyclic loading. In addition, an empirical model was derived for the evolution of the damping ratio with the cycle number, based on the laws of entropy conservation and energy conservation. From experimental results, the damping ratio of rock increased with increasing the axial strain amplitude under dynamic cyclic loading, whereas the damping coefficient decreased. Under stepped cyclic loading, the damping ratio and damping coefficient of rock increased with the increase of axial stress amplitude. It is found that the threshold for the fatigue failure of sandstone was the point where the evolution law of dissipation energy and damping changed suddenly. If the upper limit of stress was higher than the threshold for fatigue failure, all evolution curves of the dissipated energy, the damping ratio and the damping coefficient were half U–shape and characterized by three phases. On the contrary, their evolution curves were characterized by L-shape and two phases. Through the damping ratio experiments of sandstone, it is verified that the model was capable of describing the energy dissipation and the damping behavior in constant amplitude cyclic loading process.