Experimental and numerical analyses of the mechanical behavior of bonded joints can be made particularly difficult by the influence of edge effects. Therefore, understanding the stress distribution in an adhesive joint can lead to improvements in adhesively-bonded assemblies. Such an analysis is proposed in the case of usual single lap shear specimens. Stress singularities can contribute to the initiation and propagation of cracks in the adhesive. Thus, in order to obtain reliable experimental data to analyze the nonlinear behavior of an adhesive in an assembly, tests which strongly limit the influence of stress singularities must be proposed. The design and the abilities of such a device for shear tests are presented. Moreover, some experimental results obtained using a modified Arcan fixture, which has been designed to strongly limit edge effects, are presented in the case of monotonic and complex history loadings. Furthermore, a 2D non associated elasto-visco-plastic model is proposed to accurately describe the experimental behavior under tensile-shear monotonic loadings. An extension of this model is also proposed to represent relaxation type effects under shear loadings.