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Split Hopkinson pressure bar (SHPB) is one of the most important and recognisable apparatus used for characterizing the dynamic behaviour of various materials. Incident pulse generated one the incident bar usually have a rectangular shape, which is proper for some materials but for others is not. Therefore, several methods of shaping the incident pulse are used for obtaining constant strain rate conditions during tests. Very often pulse shapers made of copper or similar material are implemented due to its softness properties. In this paper such material was investigated using the FE model of SHPB. Its mechanical behaviour was characterised with and without copper disc between the striker and incident bar. Numerical simulations were carried out using explicit LS-DYNA code. Two different methods were used for modelling the copper sample: typical finite Lagrangian elements and meshless Smoothed Particle Hydrodynamics (SPH) method. As a result of two techniques used axial stress-strain characteristics were compared for three different striker’s velocity with an influence of the copper pulse shaper taking into account. Finally, FE and SPH method was compared with taking into consideration: the efficiency, computer memory and power requirements, complexity of methods and time of simulation