© 2020 Taylor & Francis Group, LLC.In this study, the adhesively bonded Single Lap Joint (SLJ) under the compressive loading is investigated to get an in-depth insight in the joint behaviour. For this purpose, three different overlap lengths, three different adherend thicknesses and also two different adherend types were used as parameters. Unlike the joints under the tensile loading, three different failure modes were found in the current joints; full plastic deformation of the adherends, failure of the adhesive layer with partial adherend plasticity, and a complete failure of the layer with full plastic deformation of the adherends. The conducted numerical analysis reveals that for correct predictions of the joint failure, it is vital to focus on some critical parts of the bonded region where stress concentrations take place in the layer. It was found that some of the SLJs under the buckling load could have both a higher strength as well as energy absorption capability, compared to those under the tensile loading.