In this paper, an analytical solution for computing the linear plastic stresses and critical temperature and pressure in a FGM hollow cylinder under the internal pressure and temperature is developed. It has been assumed that the modulus of elasticity and thermal coefficient of expansion were varying through thickness of the FGM material according to a power law relationship. The Poisson's ratio was considered constant throughout the thickness. The general form of thermal and mechanical boundary conditions is considered on the inside surfaces. In the analysis presented here the effect of non-homogeneity in FGM cylinder was implemented by choosing a dimensionless parameter, named m, which could be assigned an arbitrary value affecting the stresses in the cylinder. Distribution of stresses in radial and circumferential directions for FGM cylinders under the influence of internal pressure and temperature gradient were obtained. Graphs of variations of stress, critical temperature and pressure versus radius of the cylinder were plotted. Cases of pressure, temperature loadings were considered separately. The direct method is used to solve the heat conduction and Navier equations.