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This paper proposes an analytical buckling load formula for a cylindrical shell subjected to local axial compression for the first time, which is achieved by a carefully constructed load description and perturbation procedure. Local axial load is described by introducing an arctangent function firstly. Then, the analytical solutions of local buckling load coefficients and buckling modes for a locally compressed shell are derived after solving governing differential equations by the perturbation method. For validation, using the presented analytical buckling modes, the Galerkin method is applied to obtain numerical result, which is an infinite order determinant about local buckling load coefficient. Comparative calculation results show that local buckling load coefficients by the analytical formula are in perfect agreement with numerical ones by the Galerkin method and known results in literature. Therefore, the validity and accuracy of the presented formula are verified. Engineering application of the analytical formula is also discussed to evaluate local buckling loads of thin-walled cylindrical shell structures such as silos, pressure vessels, large storage tanks and so on.