Meshes are generated without taking account of existence of cracks in the extended finite element method. However

the enriched nodes and their enrichment types are determined by the interaction between the computational mesh and the locations of cracks. In general

the enriched nodes and their enrichment types are determined according to the enriched element types. To determine the enriched element types

the locations of cracks and the shapes of elements must be considered. The limitations judging the enriched element types with the nodal level set values only considering the locations of cracks are pointed out; and the improved method is proposed. For complex cracks

it is inconvenient to determine the enriched element types with the level set method. An effective method is proposed to determine the enriched element types

enriched nodes and their enrichment types

i.e. according to the intersection number between the cracks and element boundaries and the locations of crack inflection points

the enriched element types are determined; then the enriched nodes and their enrichment types are determined by the enriched element types. The detailed procedure of the method is presented. The case studies of numerical simulation show the correctness of the proposed method.