The modelling of the non-linear behaviour of ductile adhesives requires a large experimental database in order to represent accurately the strains which are strongly dependent on the tensile-shear loading combination. Various pressure-dependent constitutive models can be found in the literature, but only a few experimental results are available, for instance, to represent accurately the initial yield surface taking into account the two stress invariants, hydrostatic stress, and von Mises equivalent stress. This paper presents the possibility of combining the use of tests on bulk specimens and tests on bonded assemblies, which strongly limit the influence of the edge effects, with a pressure vessel especially designed to study the influence of hydrostatic stress. The latter allows pressures up to 100 MPa to be applied during mechanical testing. For a given strain rate of the adhesive, experimental results using various stress paths are presented in order to analyse the influence of the hydrostatic stress on the mechanical behaviour of an adhesive. The analysis of the results focuses herein on the modelling of the initial yield surface, but such results are also useful for the development of the flow rules in the case of 3D pressure-dependent models.