Abstract: Rock mass is a kind of geological material containing a large number of joints, cracks, faults and other structural planes. The expansion and penetration of the structural planes under stress is an important cause of rock mass failure. The numerical manifold method (NMM) can directly simulate continuous and discontinuous problems. However, in the simulation of multi-crack dynamic propagation, NMM is still in the exploratory stage. Based on the principle of linear elastic fracture mechanics, a multi-crack propagation simulation algorithm for higher-order numerical manifold method (NMM) is presented. The singularity of the crack tip displacement field was considered by adding key terms of the crack tip displacement field function to the basis function of the NMM. The stress intensity factor at the crack tip was calculated by J integral. The cracking and propagation directions of I-II mixed cracks were judged by the maximum circumferential tensile stress criterion. Hypothesis-modified multi-crack propagation algorithm was used to solve the problem of multi-crack propagation. For those integral functions which do not conform to the simplex integral form, Taylor series expansion method was used to calculate the approximate solution. The accuracy of the calculation method were verified by numerical simulation of two classical static crack propagation problems.