Abstract: The process of rock deformation and failure is essentially the process of the continuous generation,evolution and expansion of internal cracks.The study of the initiation law of multiple cracks in the rock has im portant theoretical significance and engineering value for the stability of rock mass engineering.The existence of the plastic zone at the crack tip is an important factor for the material to resist fracture.The plastic zone at the crack tip has a great influence on the crack initiation and propagation.In order to consider the influence of the crack tip plastic zone on the crack initiation law of rock,this paper derives the formula for the size of crack tip plastic zone based on the Mohr Coulomb strength criterion under the 2D stress state,and considers the hardening of the material on the plastic zone.Then based on the minimum plastic zone radius criterion,the initiation angle and the initiation load of the crack in the rock have been obtained.Finally,based on theoretical calculations,the effects of crack length ratio,crack inclination and crack spacing on the crack initiation are analyzed.The results show that the initiation angle of a compression crack under plane stress is a fixed value of 70.43°,and the initiation angle of a compression crack under plane strain increases with the increase of the hardening coefficient and Poisson’s ratio.The initiation load of a compression crack is inversely proportional to the crack length ratio and directly proportional to the crack distance.With the increase of crack inclination angle,it first decreases and then increases and its extreme point is related to the friction effect of the crack surface.The central crack is the most sensitive to the crack length ratio and the crack distance,the inner tip of the outer crack is the second,and the outer tip of the outer crack is the least sensitive.The initiation load of a compressed crack is related to the friction coefficient and the closure degree of the crack surface,and under the same conditions,the initiation load of an open compression crack is less than that of a fully closed compression crack,and the initiation load under plane stress is greater than that under plane strain.