Finite element computer programs have been used successfully for stress analysis of bodies with complex geometries and loads, and the use of these programs in cohesive fracture mechanics analysis is now widely accepted. Similar numerical procedures have been developed for use in adhesive fracture mechanics, but rather strong stress oscillations near the point of debonding have been shown to occur both analytically and numerically. This paper discusses the effect of these oscillations upon the calculation of the stress and strain energy, and demonstrates that in this potentially difficult problem, finite element codes can be used with sufficient precision for fracture analysis.