We examine and compare five constitutive models, which have been recently proposed to describe the behavior of elasto-visco-plastic fluids. The comparison is performed in simple rheometric flows, i.e. simple-shear, uniaxial elongation and large amplitude oscillatory tests and in the complex flow generated by a falling spherical particle. The first set of three models do not explicitly include shear-thinning. These are the ones proposed by Saramito [21], Park & Liu [27] and Belblidia et al. [28]. The first one has been derived under a thermodynamic framework, while the other two have been based on viscosity regularization methods. When spatial and temporal inhomogeneity are not present in the flow field, the models generally produce acceptable predictions, except for: (a) the BWW in predicting the primary normal stress under small shear rate and under small strain in the LAOStrain test, (b) all models in predicting different parts of the spectra of G' and G '', although the predictions of the SRM can be corrected when kinematic hardening is accounted for and (c) the P&L model in LAOStress because of nonexistence or multiplicity of solutions. In the complex flow, the predictions of each model are compared with the experimental data of Holenberg et al. [34] under non shear-thinning conditions and the predictions of the SRM model are clearly superior. The second set of models have been proposed by Saramito [22] to explicitly account for shear thinning either by extending the Herschel Bulkley model to include elastic effects, SRM-HB, or by introducing a PTT-type term in the constitutive model, SRM-PTT. Both these models provide acceptable results in the rheometric tests. In the falling sphere test, their predictions are compared with the experimental results by Putz et al. [15] for the settling of a particle under conditions that the Carbopol solution exhibits shear-thinning. Here the SRM-HB is found to be superior. (C) 2016 Elsevier B.V. All rights reserved.