By employing the elastic-plastic structural model introduced in part I [1], which contains four compressible bars and four elastic-plastic "hinges" of finite length, the entire dynamic deformation history of Type II structures is traced. In contrast to part I, strain-rate effects are incorporated into the analysis throughout the entire response of the structure. The Cowper-Symonds relation is adopted and the yield stress varies with the current strain-rate during the dynamic response of the model. The numerical examples presented show that the strain-rate effect plays an equally important role to that of inertia on the dynamic behaviour of this kind of energy-absorbing structure if the material of the structure is rate-sensitive, e.g. made of mild steel. Compared with the corresponding quantities in the quasi-static case, the combined effects of strain-rate and inertia make the peak load much higher and the final displacement much smaller. It is also found that because the increase of the yield stress due to strain-rate sensitivity expands the range of elastic deformation, the elastic strain energy stored in the structure made of rate-dependent material is notably larger than that in the structure made of rate-independent material. This implies that when strain-rate effects are taken into account in the analysis, elasticity must play a more significant role and should not be neglected.