This chapter investigates the axial compressive folding behavior of deployable composite cylindrical shells, establishing a theoretical model based on the Euler-Bernoulli beam model to predict load-displacement curves, shape functions, and stress levels using geometric equations combined with mathematical methods (Maclaurin series, Chebyshev polynomials). The compressive process is divided into three stages: linear elastic pre-buckling, buckling with rapid load drop, and post-buckling. Equilibrium equations, non-dimensionalization, and the Galerkin method solve for load-bearing capacity under large deflections. Experiments using T300/epoxy composite samples validate the model, showing good agreement between theoretical predictions and tests. Parametric studies reveal that increasing arc length and thickness enhances compressive load, while increasing length decreases it.