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Using Donnell non-linear shallow shell equations in terms of the displacements and the potential flow theory, this work presents a qualitatively accurate low dimensional model to study the non-linear dynamic behavior and stability of a fluid-filled cylindrical shell under lateral pressure and axial loading. First, the reduced order model is derived taking into account the influence of the driven and companion modes. For this, a modal solution is obtained by a perturbation technique which satisfies exactly the in-plane equilibrium equations and all boundary, continuity, and symmetry conditions. Finally, the equation of motion in the transversal direction is discretized by the Galerkin method. The importance of each mode in the proposed modal expansion is studied using the proper orthogonal decomposition. The quality of the proposed model is corroborated by studying the convergence of frequency–amplitude …