In this thesis , at first by using the infinitesimal theory of elasticity, the internal pressure in thick wall cylinders in the functional graded material is investigated. It has been assumed that the modulus of elasticity is varying through thickness of the FGM material according to a power law relationship. Also the value of the Poisson ratio was taken as a constant throughout the material. In the analysis presented here the effect of non-homogeneity in FGM thick cylinder was implemented by choosing a dimensionless parameter, named b, which could be assigned an arbitrary value in the cylinder. In this research, the simulation process is done using ABAQUS software. At the end of the simulation, radial and peripheral stress diagrams of pipes with functional behavior material is compared with pipes made ??of homogeneous material with the same geometrical parameters under internal pressure. By analyzing the radial and peripheral stress diagrams which obtained from the comparison of the functional behavior material with the homogeneous material, the conclusion is gained that the radial and peripheral stress in the functional behavior material is less than homogeneous material. By comparing the peripheral stresses for both materials before and after bending observed that the stress after bending increased, but the increase is negligible. Also by investigating the effect of corrosion, was found that by increasing the corrosion stresses will increase. At the end of the study, material for industries that deal with corrosive substances at different temperatures, in either case, the cylinder in concrete and soil were studied. Keywords: FGM - Infinitesimal Theory of Elasticity -Abaqus