Based on the dual equation of Hamilton system and Duhamel's integral, and the orthogonality of the deflection equations, the mechanical model of homogeneous rectangular thin plate rock mass was established. And the results showed that the effective vibration modes of thin plate granite with four sides fixed were the 1st, 5th and 6th orders under uniform dynamic load, and their vibration frequencies were 310rad/s, 975rad/s and 1309rad/s respectively. Under sustained dynamic load, moreover, the change of the vibration state of the 1st mode was the most sharp, and the positive and negative alternation of its amplitude was the most frequent in the whole period, which had the most obvious effect on the vibration of the thin plate rock mass. Based on the Fourier transform formula, the Fourier series expressions and waveforms of sustained dynamic loads which contained rectangular wave, triangular wave and impact wave were obtained. The vibration characteristics of thin plate rock mass under these three kinds of sustained dynamic loads, the dynamic distribution of deflection, stress and maximum shear stress, as well as the dynamic damage and failure modes were all obtained. The results showed that plate cracks occurred firstly in the middle of the four sides and these cracks would propagate rapidly along the boundary of the thin plate rock mass; and then, plate cracks occurred at the central of the thin plate and the main develop tendency of these cracks was outward along the long central axis, moreover, these cracks also tended to expand outward along the short side central axis. It could be concluded that the initial failure position of the thin plate rock mass could be determined by the 1st effective mode, and the development direction and trend of the damage could be determined by 5th and 6th effective vibration modes; under sustained dynamic load, tensile-shear failure occurred at four sides and shear failure at four corners; The tensile failure occurred in the central area of the thin plate, which developed into a main crack along the central long axis and a secondary crack along the short central axis, forming an " O-十" fracture pattern.