This paper presents a contribution to the development of a numerical model for an adhesive in an assembly, starting from a large data base of experimental results in the case of radial monotonic loadings. The experimental results were obtained with a modified Arcan-type fixture using specific geometries which strongly limit the influence of edge effects in order to obtain reliable information about the non-linear behavior of the adhesive. These results underline that deformations in the adhesive are much larger in shear than in peel. Thus, a non-associated 2D model, with a specific yield function, was proposed to represent accurately the experimental observations. As the stress state is not uniform in the adhesive joint for the proposed Arcan-type fixture, inverse identification techniques using non-linear finite element simulations were used. Firstly, for a given strain rate, an elasto-plastic model was proposed and its behavior was analyzed through different numerical examples. Secondly, an extension to elasto-visco-plastic models was proposed for a wide range of deformation rates under tensile-shear loading tests. Results of numerical examples and comparisons with experimental data are presented using joint-type elements (or interface elements) which allow one to limit the numerical cost in the case of bonded structures with low edge effects.