Primarily the separate distributions of elastic and perfectly plastic thermal stress in spherical pressure vessels made up of Functionally Graded Material (FGM) are represented. Next, the combined elastic and perfectly plastic thermal stress analysis of a spherical pressure vessel is considered. It is assumed that no unloading is occurred and the modulus of elasticity, yielding stress and some specific material characteristic parameters are exponential functions of radius. In a spherical FGM vessel and for different material compositions, the effect of pressure and temperature upon the growth of plastic zone is studied. Especially the change in the position of the borderline between the elastic and plastic regions is sought. In an extensive range of material thermo-mechanical properties, the position of the elastic-plastic interface line and the yield pattern, which shows the number of plasticized layers in the wall of the vessel, are indicated.

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