The constants of the Johnson–Cook and Zerilli–Armstrong material models are determined using an inverse Taylor test. In this technique, the target (specimen) and the projectile (striker) swap their positions as usually considered in the conventional Taylor test. This type of test configuration eliminates the difficulties that are normally associated with in situ heating up the specimen. The experiments are conducted at ambient and elevated temperatures under high impact velocities. The constants of the models correspond to the case when the difference between the experimental and numerical mushroomed profiles of the specimen after impact is optimized. The results indicate that Z-A model is superior to J-C model in prediction of the copper alloy deformation in the inverse Taylor test. The reason is believed to the fact that the effects of strain, strain rate, and temperature are coupled in Z-A model, but have separate effects in J-C model.