Abstract: The distribution of thermal stresses for an empty cylinder of Functionally Graded Materials (FGM) with axial symmetry is obtained, and the Genetic Algorithm (GA) is applied to the optimization problem of material composition for an empty cylinder of FGM with axial symmetry. Based on the thermal elasticity theory and computational method, the numerical calculations are made using a genetic algorithm. The minimum thermal stresses and optimum combination are obtained for an empty cylinder of FGM.