Interface damage characterization and interlaminar failure analysis of sandwich specimens with an initial interlaminar delamination in between the face sheet and the core are obtained by using interface cohesive elements. Peel tests reveal interesting particularities on damage localization and strain variation while damage is completed. The critical strain at damage initiation, as well as the critical displacement when damage is finalized, is established by using the digital image correlation method (DIC) in the cohesive zone. After the calibration of the finite element model through experimental results, the use of cohesive elements together with a linear or exponential softening law is analyzing the influence of the critical material parameters on the damage process and of the damping factor of the exponential law on the strain distribution in the core at different locations along the interface.