In this study, numerical models based on finite-element method are developed for severalapplications of fracture mechanics. The use of cracked specimens formed by differentmaterial properties has allowed us to analyse the effect of the crack position to theinterface and to have a well understanding of mismatch effect for the case of mixed modeof fracture. In other hand, we have noticed that it is very interesting to see the effectof the interface position and loading for the case of symmetrically cracked ring specimenunder compression loading.