Abstract: The numerical manifold method based on the two covers (mathematical cover and physical cover) and contact loop have been used to solve the continuum and discontinuum problems in a unified way. The mathematical cover is not enforced to coincide with the cracks when dealing with the discontinuous problem, facilitating the simulation of failure in rock mass. An enriched numerical manifold method is developed by adding the enriched displacement functions used for simulating the stress singularity to the physical patches around the crack tip. And on this base, a new algorithm of the multiple crack propagation is proposed; the overall response of the material is given during the crack propagation. Numerical examples with NMM for the classic linear elastic fracture mechanics problems are presented, suggesting that the proposed procedure is accurate and efficient.