This research employs an analytical approach to explore nonlinear torsional buckling behaviors of spiral-stiffened sigmoid FG (SSSFG) thin circular cylindrical shells. The research encompasses two variations of SSSFG cylindrical shells: those with internal and external spiral stiffeners. Furthermore, this study explores effects of two distinct material distributions for SSSFG cylindrical shells, specifically metal-ceramic-metal and ceramic-metal-ceramic layers, both following a sigmoid-law distribution. Theoretical formulations are obtained using the smeared stiffeners technique and classical shell theory, incorporating geometrical nonlinearity in the von-Kármán sense. The discretized nonlinear governing equations are obtained through Galerkin's method, and the approximate three-term solution for deflection is developed. Hence, explicit formulations are presented to ascertain the critical torsional load and depict the post-buckling torsional load–deflection curves. The outcomes of this study are validated by comparing them with the related research results existing in the literature. Significantly, the research highlights the influence of diverse parameters and the efficacy of stiffeners in enhancing the stability of SSSFG cylindrical shells. Researchers and engineers in this field may utilize the findings of this research as reference points for their design and research involving SSSFG cylindrical shells. •Nonlinear torsional buckling analyses of spiral-stiffened sigmoid FG (SSSFG) thin circular cylindrical shells.•Consideration of both the shell and stiffeners as sigmoid FG materials.•Examination of two variations of SSSFG cylindrical shells: those with external and internal spiral stiffeners.•Investigation of two distinct material distributions for SSSFG cylindrical shells, specifically MCM and CMC layers.