Abstract: As a core component of the new-generation roll-out deployable boom mechanism for deep space exploration, the bending stiffness of the spiral tube during deployment directly affects the accuracy and stability of on-orbit detection. To address the critical challenge that its geometry features a periodic variable cross-section and non-uniform interlayer wrapping constraints and rendering classical constant cross-section beam theories inadequate for accurately characterizing its bending stiffness, a theoretical modeling approach based on piecewise recursive analytical methods is proposed. Based on the actual configuration, a thin-walled cantilever beam model with variable cross-section is employed. By introducing periodic segment division and recursive boundary conditions, a piecewise continuous deflection differential equation characterized by a continuously varying moment of inertia is established. This enables an accurate analytical solution for the complex non-uniform stiffness structure. The influences of strip thickness t, strip width w, initial free-end diameter D₀, and helix angle α on the bending stiffness are analyzed. In particular, under feasible design constraints, the enhancement effects of D₀ and α on stiffness are significantly superior to that of w. Moreover, an excessively large strip width may reduce structural efficiency by limiting the feasible ranges of other parameters. The theoretical model shows good agreement with both finite element simulations (error of 4.6%) and physical experimental results (error of 6.3%), and the predicted deflection curve morphology closely matches the measured data, thereby validating the accuracy of the proposed method. This work provides a theoretical foundation for the mechanical performance optimization and engineering design of spiral tubes.