During the damage evolution of bonded joints, different modes of failure can be detected. These modes include pure modes (Mode I, Mode II, Mode III) or their combinations (Mixed-mode) according to the type and the direction of loading. Some scientifically validated test methods are commonly used to obtain the fracture toughness by loading under pure Mode I, Mode II and their Mixed-mode. Some test methods were established to obtain the fracture toughness by loading under pure Mode III, however, further research is required. The aim of this work is to clarify the mode ratio of a tubular lap joint under torsional loading and then to propose a method to determine the cohesive and damage parameters of this joint. The presumed mode of failure is Mode III, or Mixed-mode with a predominance of Mode III. Emphasis is placed on the widespread applicability of the obtained results for similar specimens loaded under similar modes.