Abstract: A new method combining the split Hopkinson pressure bar (SHPB) technique with the back-propagation (BP) neural network program is proposed. By this method, the treated strain wave signals become smooth with less noises induced by the transverse inertia. Moreover, the dynamic rate-dependent constitutive behaviour of materials can be identified, without any pre-assumption of a constitutive model. It is found that by taking the experimentally measured data of strain, strain rate and time as ‘input’ and the corresponding data of stress as ‘output’ of the BP neural network, the dynamic constitutive behaviour with internal damage or phase transformation evolution is easy to be identified, where the time could represent either the internal damage evolution or phase transformation process accompanied with the deformation process. It is emphasised that the data learnt by the BP neural network must include both loading and unloading processes, if the whole loading and unloading response is to be correctly predicted. The comparisons between the predictions and experimental results are in good agreement for both polyamide (PA) polymer (as an example of nonlinear viscoelastic materials) and Ti–Ni alloy (as an example of superelastic materials with stress-induced phase transformation).