The doctoral thesis presents the results of solving two actual problems of layered composite materials associated with tests for obtaining strength characteristics. Problem 1: two types of specimens were studied based on applying the nonlinear theory of flexible plates to obtain the interlaminar fracture toughness of layered composites. For a specimen of the thin sub-layer type, a theoretical solution was obtained in relation to the determination of the interlaminar fracture toughness for a mixed II/I mode. The fundamental possibility of using this solution in test practice was confirmed, an assessment of the advantages was given, and the problems associated with the practical implementation of tests based on this type of specimen were noted. The application of the nonlinear theory of flexible plates to the well-known standard specimen of the double-cantilever beam (DCB) was studied in more detail. A theoretical solution was obtained, an iterative algorithm for processing test results based on MATLAB code was developed, highly flexible glass fiber reinforced polymer (GFRP) specimens were tested and their comparison with the results of processing according to the ASTM D-5528-01 standard with correction of the linear solution was given. Problem 2: there was performed the experimental study of effect of plasticity of process of interlaminar delamination propagation in the layered composite of the elastic-plastic material of a matrix. Two groups of DCB glass fiber reinforced polymer specimens with brittle and plastic matrix were used. Remaining stress and strain were observed for the specimen of second group as well as smooth process of delamination growth near maximum of load.