In this paper, coupled thermoelasticity without energy dissipation in functionally graded thick hollow cylinder is presented based on Green-Naghdi theory. The material properties are supposed to vary as a power function of radius from inner to outer surface of cylinder (across the thickness of cylinder). The cylinder is subjected to heat flux heaviside function on inner surface of cylinder. A hybrid numerical method is used to solve the problem. The method is a combination of Galerkin finite element and Newmark finite difference methods. The axisymmetry and plane strain conditions are considered and the cylinder is divided to many isotropic sub-cylinders (layers) across the thickness. The functionally graded property can be created by suitable arrangement of isotropic sub-cylinders. The time history of second sounds and displacement wave propagation are obtained for various values of power function. The dynamic behavior of temperature and radial displacement distribution across the thickness are studied for certain power function exponent and various times.

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