Abstract: Based on classical correspondence principle, Mori-Tanaka and other micromechanical approaches are extended to treat the case of linear viscoelasticity in the constant thermal environment. The relaxation modulus and coefficient of thermal expansion of linearly viscoelastic FGMs are given directly in Laplace phase space, and multi-dimensional viscoelastic constitutive relation coupling thermal strain is constructed through considering the weak time-dependent feature of Poisson's ratio. Following the above work, the problem of axial symmetrical bending of viscoelastic functionally graded circular cylindrical thin shells is solved. The steady temperature field is determined taking into account of the temperature dependence of thermal and mechanical parameters. The analytic solution is derived in phase space and the creep deflection is obtained by means of Laplace numerical inversion. It is shown that the thermal effect is obvious at initial creep stage, but abates with the increase of time due to the relaxation of the thermal stresses, and the constraint effect for hinged ends is more prominent than that of clamped ends on the deflection near ends when circular cylindrical thin shell is subjected to axial compression. It is expected to give the general approach to analyze the creep deformation of viscoelastic functionally graded structures with arbitrary distribution of volume content under thermal and mechanical loading by solving above problem of axial symmetrical bending.