The main objective of this work is the numerical prediction of the mechanical behaviour up to the damage of the bends of the functionally graded material (FGM) type ceramic/metal pipes. Firstly, the effective elastoplastic proper-ties of bent FGM pipes were determined using the homogenisation law by the Mori–Tanaka models for the elastic part and TTO (Tamura-Tomota-Ozawa) for the plastic part based on a rule of mixtures per function in the form of a power law. Our work also aims at the use of a meshing method (UMM) to predict the behaviour of the FGM by finite element in the mesh of the model. The analysis was performed using the UMM technique for different loading cases and volume fraction distribution. Two stages are necessary for the analysis of the damage: the first is the model of initiation of the damage established by the criterion of maximum deformation named MAXPE and the second is criterion of the energy of the rupture according to the theory Hillerborg used to determine damage evolution. Both stages involve a 3D finite element method analysis. However, for damage, the XFEM technique was used in our UMM method to predict crack initiation and propagation in FGM pipe bends. The results of the numerical analysis concerning the mechanical behavior showed, that if the nature of the bent pipes is in FGM, a good reduction of the various stresses compared to those where the nature of the pipe is metallic material. The results were presented in the form of a force–displacement curve. The validation of the proposed numerical methodology is highlighted by comparisons of current results with results from the literature, which showed good agreement. The analysis took into account the effect of the main parameters in a bent FGM pipe under internal pressure and bending moment on the variation of the force–strain curves.