This paper presents a combined experimental and numerical study on the damage behaviour of core-shell rubber (CSR)-modified epoxy adhesives subject to high stress constraints. The test method consists of a notched axisymmetric adhesive layer loaded in tension. The stress-displacement curves of the rubber-modified adhesives have been found to exhibit a sudden reduction in stiffness after an initial linear loading region. It has been demonstrated that this corresponds to the cavitation of the rubber particles. The stress of rubber cavitation remained essentially constant at a critical hydrostatic stress of approximately 21 MPa over different rubber contents and different stress constraints. It is important to note that the rubber cavitation stress is also dependent on the size of the rubber particles, and the diameter of the rubber core is approximately 170 nm in current work. The stress constraint had negligible effect on the failure strength of the adhesive joints for the studied systems.