A mathematical model is proposed for elastic-plastic deformation of flexible cylindrical shells with spatial reinforcement structures, adapted to the use of a numerical scheme of the «cross» type. Inelastic behavior of the materials of the phases of the composition is described by equations of flow theory with isotropic hardening. The geometric nonlinearity of the problem is considered in the Karman approximation. The possible weakened resistance of reinforced shells to transverse shear is taken into account. The initial-boundary value problems, allowing determining with different accuracy the stress-strain state in the phases of the composition of fibrous shells, are formulated. The equations, boundary and initial conditions of the traditional non-classical Reddy theory follow from the obtained relations in the first approximation. The dynamic elastic-plastic flexural behavior of unidirectional-, flat- and spatial-reinforced closed cylindrical shells made of fiberglass plastic under the action of explosive type loads is investigated. It is shown that calculations on the Reddy theory can lead not only to quantitatively unacceptable, but even qualitatively incorrect results. The difference in the calculations performed by Reddy’s theory and refined theory increases with the increase of the calculated time interval. It is demonstrated that, according to the calculations by the refined theory for closed shells with a relative thickness less than 1/10, the structure with «flat» 2D-reinforcement is rational. It is shown that due to the geometric nonlinearity of the problem under study, the maximum modulo deflections in thin reinforced shells may appear much later than the stopping of the short-term dynamic load.