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Crack closure is one of the reasons inducing changes of P-wave velocity of rocks under compression.In this context,a method is proposed to investigate the relationships among P-wave velocity,pre-existing cracks,and confining pressure based on the discrete element method(DEM).Pre-existing open cracks inside the rocks are generated by the initial gap of the flat-joint model.The validity of the method is evaluated by comparing the P-wave velocity tested on a sandstone specimen with numerical result.As the crack size is determined by the diameter of particles,the effects of three factors,i.e.number,aspect ratio,and orientation of cracks on the P-wave velocity are discussed.The results show that P-wave ve-locity is controlled by the(i.e.number)of open micro-cracks,while the closure pressure is determined by the aspect ratio of crack.The reason accounting for the anisotropy of P-wave velocity is the difference in crack number in measurement paths.Both of the number and aspect ratio of cracks can affect the re-sponses of P-wave velocity to the applied confining pressure.Under confining pressure,the number of open cracks inside rocks will dominate the lowest P-wave velocity,and the P-wave velocity of the rock containing narrower cracks is more sensitive to the confining pressure.In this sense,crack density is difficult to be back-calculated merely by P-wave velocity.The proposed method offers a means to analyze the effect of pre-existing cracks on P-wave velocity.