Abstract: Coal and rock masses in deep mining would bear dynamic disturbances which propagated deeper into the coal rock mass in the form of stress wave. These stress waves were mainly composed of high order P-waves with high frequency,fast phase velocity and many wave numbers. Because of the absorption and dispersion effect in the propaga- tion of waves,the high order P-waves would change into low order P-waves with low frequency,slow phase velocity and less wave numbers. And the compressive and tensile stresses occur alternately,which could cause the strong vibration and serious damage of the coal and rock. Taking cylindrical coal and rock as an example,this paper obtained the fre- quency equation of P-waves,and established a dynamic calculation model for the displacement,strain,stress,vibration velocity and energy based on the propagation characteristics of P-waves and wave control equations. The simulation re- sults showed as follows:under the action of low order P-waves,the vibration of radial and shear stress waves were rela- tively gentle,which could be considered as an effect of quasi-static loading. Shear failure of coal-rock mass would mainly occur and distribute near the surface. Under the action of low order P-waves,the vibration amplitudes of dis- placement,strain,stress,vibration velocity and energy decreased with the increase of radius dimensionless along the ra- dial direction of the cylindrical coal rock,which followed the power function. The amplitudes of shear stress and strain were the largest,but the energy attenuation was the fastest. The authors noticed,most surprisingly,that the amplitude directions of the radial and axial stress waves were almost opposite,with the amplitude values basically same when the vibration kept stable. When there was no confining pressure,the cylindrical coal and rock mass eventually displayed crashing or splitting failure which was mainly caused by tensile stress. However,the conical failure easily occurred when there was confining pressure,which was tensile-shear failure. The maximum amplitude of displacement,strain, stress,vibration speed and energy were all located at the axis of action surface of the cylindrical coal and rock. There- fore,the initial damage position of coal and rock would be in the center of action surface.