The detachment plates 2024T3 by an Araldite adhesive is studied in this work by using the finite element method to predict the damage in traction and compression behavior under the effect of geometrical parameters such as the lap length and the geometric shape of the plates called tapered. The numerical calculation is done by the ABAQUS calculation code. The adhesive has been modeled by an element of the cohesive zone CZM which takes part of the analysis in the first place on the influence of these parameters in mixed mode such as the critical energy and the maximum stress in opening and sliding. It is well shown that the behavior and parameters evaluated condition the resistance of our bonded structure to damage. The effect of these various parameters evaluated on the resistance is presented as results by failure load curves where each value represents an analyzed model.