In order to study on rock damage caused by the confining pressure unloading, different unloading rates have been adopted in tests on the rock under the constant axial load. Emphasis has been laid on discussing influences of different unloading rates on the elastic modulus, rock strength and failure mode of the rock. The research shows that the unloading rate has exerted a prominent effect on the elastic modulus evolution of the rock, stress level at rock failure and failure mode of the rock. The greater the unloading rate is, the smaller the variation in the elastic modulus of the rock will be, indicating smaller rock damage. Similarly, the greater the unloading rate is, the smaller the corresponding confining pressure at rock failure will be, implying the greater stress deviator imposed on the rock, in which case, the rock failure will be more abrupt and energy release more violent.