Abstarct: Cracking and fracture is very important issue in today's industrial world. During history, many disasters have been occurred including airplanes crash, buildings and bridges collapsing, getting off the trains from the rail and etc which is due to creation of cracks and their propagation under incoming loads and have been caused to creation of abundant financial and human health damages, disturbing a part of transportation system and many other problems. Therefore it is very essential to understanding the behavior of crack and predicting the process of it’s propagation for constructing the industrial components, underground structures and other tools and objects that are valuable for human. The branch of science which deals with analysis and study of these problems is called fracture mechanics. With the passage of time and advancement of science, human faces newer problems in real world everyday including fracture machanics problems with complex geometries which their analyzing and checking by using experimental and field works is very hard or impossible; So the need of using numerical computational methods with more precision is being felt. Extending the finite element method has been one of the most important developments in the field of numerical methods which has been used for a long time to analyze the engineering problems. Because of arbitrary paths that crack passes in each step of it’s propagation under mixed mode loading conditions, in conventional finite element method at each step of crack propagation, remeshing must be done to lead crack geometry matches with elements boundaries which is the main defect of this method. Now according to the existent limits in finite element method and other mesh-baxsed methods for analyzing the problems like large deformations and cracks propagation, in this research the Extended Element Free Galerkin method (XEFG) has been used which is one of the global weak form meshfree methods. In the mentioned method, no element and no mesh have been used for defining the problem domain and approximation functions have been constructed just by using the set of uniform distributed nodes in the domain of the problem and on the boundaries. In this method, appropriate enrichment functions have been added to the approximation of standard element free galerkin method. In the mentioned method, the approximation of Moving Least Squares (MLS) has been used for constructing the shape functions and also the used weight function in the shape function has been the quartic spline. The Level Set method has been used for modeling and showing the crack body and chasing the path of it’s tip. Also in this research the interaction integral or M integral has been used for calculating the stress intensity factors in pure and mixed modes. The path of crack propagation has been determined with using the maximum circumferential stress criterion in each step of crack propagation. By using the above method, the relevant code has been written in MATLAB® environment and also the numerical examples have been presented in two sections with the names of stationary cracks and propagation of cracks; in these examples by changing the different parameters such as the used set of nodes, their effect on the accuracy of obtained solution and it’s error rate has been shown. Finally the obtained results from stress intensity factors in pure and mixed modes and equivalent mode-I stress intensity factor have been compared with existent results in past researchers studies which this validation indicates the accuracy and precision of the written codes and generally the work has been done in this research.