In order to evaluate the shear bond strength of a steel-concrete joint using an epoxy adhesive interlayer, push-out tests were carried out. The test samples consisted of two sandblasted steel plates and a self-compacting concrete sample, with the epoxy layer applied on the steel plates and gritted with granulates. During testing, an external force was applied to the concrete core and continuously recorded. To investigate the failure mechanism in detail, a fracture mechanics approach is required. In this paper theoretical-numerical assessment of the push-out test is performed. Regarding the finite element calculations, the locations suitable for failure initiation match bi-material (steel-concrete) notches. The most dangerous locations are evaluated from a generalized linear elastic fracture mechanics point of view. The critical load corresponding to the conditions of failure initiation is estimated and compared with the experimental results.