Based on the method of time steps, a numerical-analytical model of viscoelastic-plastic deformation of circular cylindrical shells with spatial reinforcement has been developed. Instant plastic deformation of the materials of the components of the composition is described by the theory of flow with isotropic hardening. The viscoelastic deformation of these materials is described by the governing equations of the Maxwell – Boltzmann model of the body. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The possible weak resistance of composite shells to transverse shears is taken into account on the basis of the Ambardzumyan theory. The developed model of the mechanical behavior of materials of the components of the composition is adapted to the use of an explicit numerical “cross” type scheme. The viscoelastic-plastic and elastoplastic dynamic and quasistatic deformation of thin flexible fiberglass cylindrical shells under the influence of internal pressure, as well as rectangular elongated plates under the action of a uniformly distributed transverse load, are studied. The constructions have traditional reinforcement structures with orthogonal laying of fibers on equidistant surfaces or have spatial reinforcement structures. It is demonstrated that calculations performed on the theory of elastoplastic and rigid-plastic deformation of reinforced shells and plates do not give even an approximate idea of the residual states of composite constructions under their dynamic loading. It is shown that, after viscoelastic-plastic dynamic deformation, relatively thin reinforced constructions acquire corrugated residual forms. With quasistatic transverse loading of composite plates, the residual deflection has a traditional form, i.e., folds are not formed.