Abstarct: In this study, to calculate stress intensity factors for longitudinal semielliptical cracks in the thick-walled cylinder FGM using the weight function method has been subjected to thermal load. For this purpose, finite element simulation is done in Abaqus software and radial, environmental, and von Mises stresses along the cylinder thickness. The finite element results were compared with analytical results and a good agreement was obtained. The stress intensity factors are derived from finite element simulation was compared with relation Anderson and good agreement was reached. Then, to determine the weight function governing the problem of the relationship proposed by Shen and Glnika is used. For this purpose, the functionally graded cylinders with different coefficients and crack depth in Abaqus software simulated. Then, using the finite element results, relationship proposed by Shen and Glnika coefficients that depend on the geometry, load, crack length and material of cylinders were extracted.