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A theoretical explicit formulation for numerical simulation of the buckle propagation in deepwater pipelines is proposed. It is based on thin shell theory incorporating large rotations and material elastic-plastic behavior for infinitesimal strains. The equilibrium equations are solved numerically through a computer program using the finite difference method associated to the dynamic relaxation technique. The pipe post-buckling behavior is determined by the arc-length method used in convolute regions of the load-displacement curve. The numerical results are correlated with experimental data from small scale laboratory tests.