Recent short pulse (femtosecond) laser experiments have shown the existence of a so called superelastic precursor for short time periods after shock wave formation. The superelastic precursor is characterised as having amplitude far greater than the Hugoniot Elastic limit. This work reviews the current orthotropic thermoelastic plastic-damage model developed at Cranfield University, which includes the ability to model high velocity, shock wave forming impacts. The current model is unable to reproduce the superelastic precursor. Recent methods of looking at plasticity are reviewed and model improvements are suggested to enable the Cranfield model to reproduce superelastic precursor waves. The methods investigated are both dislocation based as it is determined that it is necessary to model deformation on the microscale in order to achieve reproduction of phenomena on the timescales of the early stages of shock wave formation and propagation. The methods investigated are the so-called self-organisation of dislocations and a mobile and immobile dislocation method proposed by Mayer. The plasticity part of the model proposed by Mayer is suggested for further investigation, including implementation into the DYNA 3D hydrocode which contains the current Cranfield model, to numerically asses the models capabilities. Similar, the self-organisation model is put forward for further numerical analysis. Further, calculation of the continuum Cauchy stress using purely atomistic variables is investigated in the form of the virial stress. It is determined that the virial stress calculation is unsuitable for modelling shock waves, however an alternative atomistic stress calculation which is more suited to shock waves is discussed. It is proposed that this stress calculation could be used to investigate the stresses contained within the thin shock front.