We present a cohesive zone model for delamination in thin shells and composite structures.The isogeometric (IGA) thin shell model is based on Kirchhoff-Love theory.Non-Uniform Rational B-Splines (NURBS) are used to discretize the exact mid-surface of the shell geometry exploiting their C1-continuity property which avoids rotational degrees of freedom.The fracture process zone is modeled by interface elements with a cohesive law.Two numerical examples are presented to test and validate the proposed formulation in predicting the delamination behavior of composite structures.