<p>Circumferentially functionally graded (CFG) cylinders, as novel composite structures, require a clear understanding of their mechanical properties for structural design and optimization. This paper uses the state-space method and Fourier differential quadrature method to derive semi-analytical elastic solutions for CFG cylinders with arbitrary circumferential functionally graded properties. Based on two-dimensional elasticity theory, state equations of CFG cylinders containing cross-coupling terms are derived. The Fourier differential quadrature method and laminate approximation model are used to handle the variable-coefficient terms in the equations, resulting in solvable ordinary differential state equations with constant coefficients. A numerically stable method is applied to obtain exact solutions of the state equations, avoiding common numerical instability issues in semi-analytical methods. The proposed method is applied to solve numerical examples of three different configurations of CFG cylinders, and the computational results are compared with finite element method (FEM) results to verify the method’s convergence and accuracy. The results demonstrate that the proposed method can achieve precise computational outcomes with relatively fewer nodes.</p>