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The problem of delamination growth in composite materials is considered by author applied to cylindrical shells. This type of defect causes a decrease of rigidity, strength, stability of the structure and determines its durability and reliability. Formulation of delamination growth problem is performed in a three-dimensional case taking into account large displacements. The interaction between individual layers of material is modeled through contact interaction which is described by the constitutive relationship. Algorithm and ways to solve the initial-boundary value problem is suggested by the author.