In this paper, an analytical method is developed to obtain the solution for the one dimensional transient thermal and mechanical stresses in a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r but the Poisson’s ratio is assumed to be constant. Transient temperature distribution, as a function of radial direction and time with general thermal boundary conditions on the inside and outside surfaces, is analytically obtained for different layers, using the method of separation of variables and generalized Bessel function. A direct method is used to solve the Navier equations, using the Euler equation and complex Fourier series. This method of solution does not have the limitations of the potential function or numerical methods as to handle more general types of the mechanical and thermal boundary conditions. Manuscript profile