<p>Uncertainty in the natural frequencies of composite cylindrical shells is typically assessed with parametric models that assume specific probability laws for material and geometric inputs. Here, we propose a fully data-driven, nonparametric alternative based on the orthogonal bootstrap, integrated into a semi-analytical Rayleigh–Ritz framework for shells subjected to axial load and internal pressure. This study makes four key contributions: (1) It introduces the orthogonal bootstrap to the structural dynamics of composite shells, enabling uncertainty propagation directly from empirical samples without prescribing distributions; (2) it provides a head-to-head comparison between the nonparametric approach and a conventional parametric Monte Carlo scheme (Beta-distributed), clarifying the conditions under which each method is most advantageous; (3) it incorporates stress-stiffening effects (geometric stiffness) from axial compression and internal pressure into the Rayleigh–Ritz formulation, enabling probabilistic frequency estimates under combined loading; and (4) it validates the semi-analytical results against a refined finite-element model, demonstrating an order-of-magnitude reduction in computational time with orthogonal resampling. The results reveal that frequency variability is primarily dominated by the radius-to-thickness ratio and fiber elastic modulus, while density predominantly influences mass-driven shifts. The proposed framework offers a transparent, efficient means of quantifying uncertainty in composite shell dynamics without the risk of distributional misspecification, and it can be readily extended to other laminated configurations and loading scenarios.</p>