<p>In this paper, the static analysis of the functionally graded carbon nano-tube reinforced composite (FG-CNTRC) cylinder shells with different boundary constraints under thermomechanical reactions is conducted. Using the temperature-dependent material characteristics, the quasi-three-dimensional high-order shear deformation model, and taking the normal stress effect into consideration, the governing equations are established. In which the temperature is considered to change along the thickness, and then the distribution law is determined based on the temperature transfer equation and temperature boundary constraints. An analytical solution that uses a single trigonometric series and Laplace transform is used to tackle fundamental equations for the shells with various boundary constraints. The proposed approach is confirmed by evaluating with available data of other researchers. The influences of material parameters, geometrical parameters, and gradient thermal loads on displacement and stress in the shell are investigated, which focuses on stress analysis at the clamped edge. Some fascinating results are found, such as the effect of internal pressure load on normal stress opposite that of thermal load on the inner surface; the influence of thermal effect on longitudinal stress is small compared with that of internal pressure load at the clamped boundary area; the stress components have a sudden jump in value at the clamped edge area. The findings of this work have significant implications for the computation and design of cylindrical shell concepts composed of advanced materials, while also considering the influence of temperature variables.</p>