In this article, static analysis of clamped-clamped (C-C) functionally graded carbon nanotubes reinforced composite (FG-CNTRC) cylindrical shell subjected to external pressure was conducted. The governing equations were established by using higher-order shear deformation theory (HSDT) taking transverse normal stress effect into account. In this theory, the transverse displacement w is not a constant but rather is the second order polynomial of the coordinate along the thickness direction. Distribution of carbon nanotubes (CNT) across the shell thickness is assumed to be uniform (UD) or functionally graded in four types: FG-Ʌ, FG-V, FG-O, and FG-X. Effective material properties of FG-CNTRC cylindrical shells were estimated by the rule of mixture. An analytical solution using the simple trigonometric series and the Laplace transformation to solve governing equations of shell with clamped boundary condition at the both ends is presented. The validation of the applied approach was examined by comparing the results based on 3D exact model. The effects of the CNT distribution, the CNT volume fraction, and the geometrical parameters on the static behaviour of cylindrical shells subjected to external pressure were investigated. The result is remarkable that the stress components near the outer or inner surface vary most strongly, and in the case of a short or/and thick shell, the geometric parameter greatly affects the stress of shell.