Abstarct: Considering the fact that functional graded materials are categorized among the newest material in the world, it is necessary to analyze their behavior and properties more accurately. Dynamic fracture mechanic is one the mechanical branches that attracted the attention of researchers during last century to analyzes the behavior of fracture in material. The current thesis, using the extended finite element method (XFEM) i,e, one of the numerical methods in the analyzes of fracture, investigates the dynamic of stress intensity factor in cylindrical conservators in great detail. In this thesis after functional graded materials detection and their behaviors the finite element method is investigated. In following the extended finite element method (XFEM) is introduced and its application in fracture mechanic problems and simulation of fractures with regular micromechanical method for complex material with using the generalized isoparametric elements are studied. Afterward, equilibrium equations in cylindrical coordinates for axisymmetric scenario with XFEM is presented in discrete matrix style and solved with Newmark method. In this dissertation, interaction integral is used to obtain the stress intensity factors. All of the solving steps from creation of mesh up to solution and results part, displacement contours and stress tensors are solved with MATLAB scientific program. Accuracy of the results is checked against some other well-known publications. Finally effects of length of fracture, change of properties, rotational speed and radii of cylinder in static loads on stress intensity factor. Also variation of stress intensity factor against time in dynamic load scenario is depicted. The material in this investigation in considered be glass epoxy.