Delamination is typically modelled using cohesive zone models. In this paper, it is shown that the validity of most models is limited to small displacements and/or deformations at the interface and the surrounding bulk materials. A large displacement formulation (LDF) is proposed that overcomes issues of the classical formulation with large displacements and deformations at the interface. Subsequently, a 3D cohesive zone element with this LDF is introduced and its numerical implementation is elaborated. Then, a 3D FEM model is proposed and the determination of several model parameters is substantiated. Finally, the implementation is validated by comparing numerical results with experimental observations.