The paper presents a comparison of the cohesive zone model (CZM) and the continuum damage mechanics approach in predicting the static failure of a single lap joint (SLJ). The effect of mesh size and viscosity were studied to give more understanding on the failure load and computational time. Both the load-displacement response and the backface strain technique were utilised to compare the validity of predictions. Peel and shear stress and damage distributions along with the damage progression are compared to understand the behaviour of the models in predicting the static failure response. In general, both approaches show good accuracy in predicting the failure load; however, the cohesive zone approach requires shorter computation time than the continuum damage approach. The continuum damage approach shows some mesh-dependency particularly for elements with high aspect ratios, whereas the cohesive zone approach is not. The continuum damage approach is less sensitive than the cohesive zone approach to the artificial damping required to achieve convergence. Another interesting finding is using the same ultimate stress level of damage in the continuum damage approach at the peak load is much lower than that in the cohesive approach; but the failure process in this approach is faster.