The static and kinematic shakedown of a functionally graded (FG) Bree plate is analyzed. The plate is subjected to coupled constant mechanical load and cyclically varying temperature. The material is assumed linearly elastic and nonlinear isotropic hardening with elastic modulus,yield strength and the thermal expansion coeffcient varying exponentially through the thickness of the plate. The boundaries between the shakedown area and the areas of elasticity,incremental collapse and reversed plasticity are determined,respectively. The shakedown of the counterpart made of homogeneous material with average material properties is also analyzed. The comparison between the results obtained in the two cases exhibits distinct qualitative and quantitative difference,indicating the importance of shakedown analysis for FG structures. Since FG structures are usually used in the cases where severe coupled cyclic thermal and mechanical loadings are applied,the approach developed and the results obtained are significant for the analysis and design of such kind of structures. The static and kinematic shakedown of a functionally graded (FG) Bree plate is analyzed. The plate is subjected to coupled constant mechanical load and cyclically varying temperature. The material is assumed linearly elastic and nonlinear isotropic hardening with elastic modulus, yield strength and the thermal expansion coeffcient varying exponentially through the thickness of the plate. The boundaries between the shakedown area and the areas of elasticity, incremental collapse, respectively. The shakedown of the counterpart made of homogeneous material with average material properties is also analyzed. The comparison between the results obtained in the two cases exhibits distinct qualitative and quantitative difference, indicating the importance of shakedown analysis for FG structures. and the results obtain ed are significant for the analysis and design of such kind of structures.