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In this paper static and dynamic problems of the theory of cylindrical shells are studied at cross-section non-uniform loads. Problems are investigated by two methods: analytically (in the ranks of) and Bubnov-Galerkin s method in the maximum approach. Good concurrence of results received by both methods for linear stationary pronlems is shown, it allows to assert, that results received with the help of Bubnov-Galerkin s method possess high accuracy thai enables to investigate the broad audience of problems. For vector/ally nonlinear problems (tasks) of a statics and dynamics the decision is received by Bubnov-Gaier kin s method in the maximum approach.