1D nonlinear model of a thin plate (or beam) with delamination was developed earlier. Large deflections and membrane strains of a plate in buckled state, as well as the strain energy described using elliptic integrals. The Griffith-type energy condition was used as a criteria of delamination propagation. The analysis of the destruction of the plate was performed depending on the geometrical dimensionless parameters of a plate and the material strength performance. Here the mentioned model is extended to the general mode of delamination and it allows to describe the post-buckling stage and damage propagation. Model application as a base for the alternative determination of the interlaminar fracture toughness of the layered composites is indicated.