Applicability of constitutive models of Cowper–Symonds (CS), Modified Cowper–Symonds (Modified CS), Johnson–Cook (JC), Zerilli–Armstrong (ZA) and Tanimura–Mimura 2009 (TM2009) is discussed by comparing the properties of these models with experimental data. It is shown that the stress–strain curves at each strain rate, which are predicted by using the values of parameters published in the literature for the CS, MCS, JC and ZA models, can sometimes diverge from the experimental curves, not only for the large strain region near the true fracture strain, but also for the homogenous deformation region. It is only necessary to know the quasi-static stress–strain curve in advance for the TM 2009 model, because the set of parameters is given for each material group, and can be used for any material belonging to the group. Simple methods to estimate the quasi-static curve are discussed.