---

A new approach is proposed to model a crack in orthotropic composite media using the extended finite element method (XFEM). The XFEM uses the concept of partition of unity in addition to meshless basic idea of approximating a field variable by its values at a set of surrounding nodes. As a result, higher order approximations can be designed with the same total number of degrees of freedom. In this procedure, by using meshless based ideas, elements containing a crack are not required to conform to crack edges. Therefore mesh generating is performed without any consideration of crack conformations for elements and the method has the ability of extending the crack without any remeshing. Furthermore, the type of elements around the cracktip is the same as other parts of the finite element model and the number of nodes and consequently degrees of freedom are reduced considerably in comparison to the classical finite element method. Developed orthotropic enrichment functions are further modified to enable modeling isotropic problems.