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The material structure of laminated vibration damping steel sheet(LVDSS) was introduced in detail. An interface cohesive model between the skin sheets was developed by using a contact/interface approach, and the model was applied to simulate "T"-peel and lap-shear processes of LVDSS. The interface contact stress distribution during the "T"-peel and lap-shear processes is obtained, and the finite element analysis(FEA) results agree satisfactorily with the corresponding experimental results. As a result, the model is suitable to simulate the cohesive of LVDSS