The split Hopkinson pressure bar (SHPB) technique and the wave propagation inverse analysis (WPIA) technique are both extensively used to experimentally investigate the impact behavior of materials, although neither of them alone provides a fully satisfactory analysis. In the present paper, attention is given to new experimental techniques by incorporating a damage-modified constitutive model into the SHPB technique and combining the Hopkinson pressure bar (HPB) technique with WPIA. First, to distinguish the response due to dynamic constitutive behavior and the response due to dynamic damage evolution, the SHPB method incorporating a damage-modified constitutive model is developed, including an explicit damage-modified Zhu–Wang–Tang model and an implicit damage-modified constitutive model. Second, when the SHPB results become invalid, a method of combining new Lagrange inverse analyses with the HPB technique is developed, including cases of the HPB arranged in front of a long specimen and behind the specimen. As examples of these new methods, typical results are given for nonlinear viscoelastic polymers and concretes considering damage evolution, a super-elastic Ti–Ni alloy with phase transformation and an aluminum foam with shock waves propagating within it.