The application of bonded joints is increasing due to their several advantages to alternative bonding methods. As a result, more efficient predictive tools are necessary to increase the confidence of designers. In this context, cohesive and continuum damage models acquire special relevancy owing to their capacity to simulate damage onset and growth. Both of these methodologies combine strength of materials with fracture mechanics, thus overcoming the limitations of each method. A cohesive mixed-mode damage model based on interface finite elements and accounting for ductile behaviour of adhesives is presented. The cohesive parameters of the constitutive softening law are determined using an inverse method applied to fracture characterization tests under pure modes, I and II. In this context a new data reduction scheme based on crack equivalent concept is developed and applied to fracture characterization tests. Good agreement between the numerical and experimental results was obtained for strength versus overlap length in single-lap joints. A continuum mixed-mode damage model is also presented using a triangular softening law adequate only for brittle or moderately ductile adhesives. In these models the material properties degradation occurs inside of the solid elements, which is advantageous relatively to cohesive methods mainly when damage propagation onset and path are not known a priori. (c) 2008 Springer Berlin Heidelberg.