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Given the field of application and the many advantages, the use of FGM (Functionally Graded Materials) materials has recently been extended in several components and more particularly in cylindrical structures, which have been the subject of several recent studies. Our work aims to use the finite element method to analyze a cylindrical structure in FGM with properties gradated in the direction of the radius (Thickness) solicited purely in internal pressure by the implementation of a UMAT subroutine in the calculation code ABAQUS. The elasto-plastic behavior of the FGM is described by the flow theory represented by the equivalent stress of Von Mises and an incremental hardening variable. The TTO model (Tamura-Tomota-Ozawa) was used only to determine the elastic-plastic properties of the FGM material. The radial, tangential and axial stresses according to the thickness were evaluated in the first part of our work. In the second part, these stresses are evaluated under the same conditions but with the presence of a micro-cavity. The results obtained show clearly that these stresses are in direct relation not only with the thickness and properties of the FGM tube but also with the presence of the cavity.