Abstract: Two approaches are usually used in the studies of dynamic constitutive relation of materials. One is to determine the constitutive relation from the wave propagating signals (the so-called second class of inverse problems). The another is to de-couple the stress wave effects of structures and the strain-rate effects of materials. In both approaches, stress wave propagation plays a key role. In the present paper, some important aspects associated with this problem are discussed, particularly in relation to the SHPB technique. Both the assumption of uniform distribution of stress and strain along the specimen and the assumption of uniaxial stress are analyzed in detail.