Studies of the properties of materials at high strain rates by the split Hopkinson pressure bar suggest that most materials show a sharp increase in strain rate sensitivity at high rates. In this paper, analytical and numerical evidence is presented which shows that his apparent increase in the strain rate sensitivity reported in the literature may result from stress wave propagation effects present in the test. A one-dimensional analytical solution has been developed for a rate independent bi-linear material tested in a split Hopkinson pressure bar apparatus. The solution, which is based on a stress wave reverberation model, shows that there is an apparent increase in the strain rate sensitivity of the material which can only be explained in terms of large propagating plastic wave fronts in the specimen. Numerical modelling of the same test geometry for the same input material model is in excellent agreement showing conclusively that stress wave propagation effects are inevitable at high impact velocities. The assumption of uniform stress and strain distribution within a split Hopkinson pressure bar specimen is therefore incorrect at high impact velocities. The formulation of the novel numerical code used in the present work, which is based on the finite volume technique, is also presented.