This work focuses on modelling the rate-dependent response of adhesively bonded structures. An experimental study undertaken in parallel with this has provided material data defining both the tensile and shear response of the adhesive system. In addition, instrumented data for a range of single lap joints was also available. Three different rate-dependent material models have been assessed as part of this work. Whilst the rate-dependent von Mises material model was easiest to implement, it was found that it could not model the shear data using the tensile data due to hydrostatic stress sensitivity in the adhesive. Difficulty was experienced in obtaining a converged solution for the rate-dependent hydrostatic stress-sensitive material model provided by ABAQUS. However, an overstress-based visco-plastic model developed in a previous programme was able to model both the tensile and shear data correctly. Two of these models were then used to simulate the various single lap joints tested and it appeared that the von Mises model gave closer predictions than the visco-plastic model. A possible reason for this was damage within the joint that was not modelled but this aspect was not pursued. Finally, it was shown that a rate-independent strain-based failure criterion appeared to give good predictions of joint strength in most of the configurations considered.