A revision of the basic assumptions those are usually used in the analysis of stability of thin delaminated layer and delamination propagation in a compressed composite is presented in this paper. For this purpose, the theory of flexible elastic plates with large displacements was used. As a result the compressive force and the total longitudinal strain of sub-laminate are expressed in terms of complete elliptic integrals, which uniquely identify the buckled shape of sub-laminate, the effect of buckling on the compression strain and increment of the compressive force in the buckled state. Stress and strain, as well as the strength of the buckled sub-laminate in the dangerous cross-section were also analyzed. The results of the general analysis of delamination propagation and its compression-bending destruction in the buckled state allow to define the basic regularities of the damage behavior of compressed layered composite.