In this paper, FGMs are used as non-uniform materials in high temperature environments specially in various industries like aircraft, aerospace vehicles, nuclear plants and engineering structures. Different industries use them in thin and thick walled spherical pressure vessels. Based on the governing equations, differential equation of stresses is obtained in plastic state that can be widely used in the study of vessel and pipe behavior in elasto- plastic state. It is discussed on the temperature distribution and stress - strain relationships in the tube under internal pressure and temperature difference. Properties of these materials are considered as variable parameters function of radius. In this work, effects of these parameters have been investigated on yielding and the yield temperatures and stress changes under different loading in during thickness of the tubes. Furthermore it is shown that tubes structure can be optimized by choosing appropriate parameters. In fact, by study the four parameters, internal and external temperature, internal pressure and the yield stress, together, can be better analyzed on a functionally graded cylindrical tube that this work has been shown at the end of the article.