The stress singularity at the theoretical point of maximum stress in an uncracked single lap joint is analysed by a finite element method. By treating the interface corner of a bonded joint (between adherend and adhesive) as a perfectly bonded wedge and using a fracture mechanics method, considerable advantages over other continuum mechanics approaches for investigating the bondline thickness effect on joint strength are shown. This study has essentially two aims: (i) determination of the strength of the singularity by finite element analysis and comparison with the analytical prediction of Bogy for varying bondline thickness; and (ii) determination of stress intensity factors for varying bondline thickness. Good agreement is shown between the numerically-calculated strength of the singularity with the analytical value obtained from Bogy. The calculated stress intensity, after an initial decrease in the low bondline thickness range, is found to increase with increasing bondline thickness. This agrees well with the trends predicted by experiments.