Abstarct: Today, the composite structures are common structures in various sciences such as engineering, military, medical, etc. The most common reason of failure in composite structures is occurrence of crack propagation. The initial crack in the structure is one of the most important and effective factor in occurrence of failure. Crack propagation is an important issue that should be examined and tested by researchers and engineers. Therefore, by knowing enough about this phenomenon, we can prevent annually huge damages caused by crack propagation in various parts. The extended finite element method is convenient and practical which attracted the attention of many researchers in Evaluation of crack propagation. The done works in this study can be classified in two main parts including checking the crack propagation behavior in two common engineering examples such as three point bending beam and indentation test with regard to the elastoplastic behavior. Examined modeling in this study has been done by ABAQUS software and analysis was performed by using the extended finite element method. In reviewing of first example, the impact of two parameters such as young’s modulus and fracture energy in three point bending beam of one laxyer was studied. By increasing the amount of fracture energy in three point bending beam, crack propagation will occur for more loads. Also, as value of young’s modulus is increased, it will lead to brittle behavior in three point bending beam. In the following, by adding laminated laxyer to a single laxyer beam, crack propagation will be discussed to site hard laxyer on soft laxyer and vice versa in this the composite structure. By wrapping a hard laxyer on soft, the maximum amount of maximum load on the load-displacement graph will be increased and three point bending beam will tolerate more load until the moment of crack propagation. In the final part of this example, sensitivity analysis will be done to increase the thickness of the coating laxyer for putting hard laxyer on soft laxyer and vice versa. By increasing the thickness of the coating laxyer in being of hard laxyer on soft laxyer, the elements of coating laxyer become more involved in freight and crack propagation will occur by more loads. In order to check crack propagation between laxyers in composite structures, three-dimensional modeling of indentation test has been done. In the first part of indentation test modeling, the sensitivity analysis for wrapping a laxyer with more submission stress on a laxyer with less submission stress and vice versa, has been shown on load-displacement graph. In the following of this example, the impact on putting first crack in intersection of coating laxyer and undercoating laxyer on load-displacement graph has been considered and it was observed the presence of initial crack that causes reduction of freight capacity in the example has been studied. By regarding to coating laxyer and undercoating laxyer, the consideration of impact of putting hard laxyer on soft laxyer and vice versa on crack propagation had been done and it was resulted that more hard coating laxyer more crack between laxyer. In the final part of this example, a sensitivity analysis was conducted for the thickness of the coating laxyer on the load-displacement graph and it was observed by increasing the thickness of wrapping laxyer in being of hard material on soft material, the sample has more freight ability. By increasing the thickness of wrapping laxyer in being soft laxyer on hard laxyer, the capacity or ability of sample’s freight will be decreased.