In the present research, an internal semi-elliptical surface crack in a FGM thick-walled cylindrical vessel under internal pressure is assumed. The Poisson ratio is constant throughout the vessel and the material is considered to be isotropic with exponentially varying elastic modulus. The KI is calculated using the BEM and FEM for different values of the relative depths of crack and material gradients. The research results show that increasing the E2/E1, decreases SIF and when E2/E1 = 10, the SIF of the FGM vessel is often lower than the corresponding homogeneous vessel. It can be observed that the relation between KI and internal pressure in FGM is linear as for homogeneous materials, so that increasing internal pressure KI increase as the same. The obtained results of BEM and FEM methods show that good agreement between the results can be seen.
