This work is aimed at analyzing and comparing the suitability and precision of some interface failure criteria for predicting adhesive failure onset on structural adhesive joints. The comparison is based on the predictions of the criteria for the failure for the failure onset in tests that assure an adhesive failure. The tests are peeling and torsion/tension tests with butt joints with different geometries. For the prediction, stresses calculations are made in the finite elements software, COMSOL Multiphysics 3.3. The criterion which best fit the experimental data involves both the interface stresses and the energy released by the spontaneous presence of a crack. This original criterion seems to be suitable for predicting failure of interfaces in different geometries of structural joints subjected to any failure condition whereas an average stress criterion is not suitable for this task.