The functionally graded materials (FGM) applications in engineering become more and more important in the future. The FGMs are composite materials where the microstructures are locally varied. The composition and the volume fraction of FGMs constituents vary gradually, giving a non uniform microstructure with continuously graded macro properties. Details of design, processing and applications of FGMs can be found in [
]. In order to be able to predict the damage and strength degradation, an understanding of the temperature distribution is important [
]. In this paper, a pversion of the finite element method is considered to determine the steady state temperature distribution in functionally graded materials. The graded Fourier p-element is used to set up the one dimensional heat conduction equations. The temperature is formulated in terms of linear shape functions used generally in FEM plus a variable number of trigonometric shapes functions [
] representing the internals degrees of freedoms. In the graded Fourier p-element, the function of the thermal conductivity is computed exactly within the conductance matrix and thus overcomes the computational errors caused by the space discretisation introduced by the FEM. Explicit and easy programmed trigonometric enriched conductance matrices and heat load vectors are derived by using symbolic computation. The convergence properties of the graded Fourier p-element proposed and the results of the numbers of test problems are in good agreement with the analytical solutions. Also, the effect of the non-homogeneity of the FGM on the temperature distribution is considered.