In this study, a neural network is applied to optimization problems of material compositions for a nonhomogeneous hollow circular cylinder with arbitrarily distributed and continuously varied material properties such as those of a functionally graded material. Using the analytical procedure of a laminated hollow circular cylinder model, the analytical temperature solution for the cylinder is derived approximately. Further more, the thermal stress components are formulated under the mechanical condition as being traction-free and making use of the Airy's stress function method. As a numerical example, the hollow circular cylinder composed of zirconium oxide and titanium alloy is considered. In addition, for the optimization problem of minimizing the thermal stress distribution, the numerical calculations are made using a neural network and the optimum material composition is determined taking into account the effect of the temperature dependency of material properties. Furthermore, the results obtained by the neural network and the ordinary nonlinear programming method are compared.