In this study, our previous experimental study was extended applying the exponential Drucker-Prager (EDP) yield criterion to define the numerical failure loads for mono and bi-adhesive single lap joints (SLJs) [Oz and Ozer, 2016]. Bi-adhesive (or hybrid adhesive) joint is an alternative stress-reduction technique for adhesively bonded lap joints. The joints have two adhesives with different moduli in the overlap region. Non-linear finite element analyses were carried out for mono and bi-adhesive joints implementing the EDP material model. Distributions of EDP maximum principal stress, equivalent stress and shear stress were obtained along the middle of the adhesive thickness. Numerical failure loads were compared with our previous experimental failure loads. In addition, hydrostatic stress and equivalent plastic strain distributions for these joints under the failure loading were obtained. The general results show that experimental and numerical, failure loads were in a good agreement. As a result, when bond-length ratios are selected properly and appropriate adhesives are used along the overlap length, the strength of bi-adhesive joints, compared to mono-adhesive joints, was found to increase considerably.