Problems of selection and application of classical and refined theories of composite structures for solving problems of stress-strain state calculation for laminated plates, circular and eccentric rings are considered. Approaches used for obtaining numerical solutions are presented. It is demonstrated that selection of a reference surface has a considerable impact on plate stress-strain state numerical analysis results. It is also found that modeling techniques of plate loading and fixation have to be taken into consideration. Finally, ranges of values of mechanical properties and geometrical parameters are evaluated wherein the use of refined plate theories are required. Particularly, it is necessary when construction has geometrical «features» (small radii of inner hole, displacement of hole center), and its composite materials have markedly different mechanical properties of components.