We present a systematic analysis of the predictions of two tube-theory based constitutive models: Marrucci and Ianniruberto and Rolie-Poly models. These models are tested in their single-mode form in rheometric flows and in their multimode form in transient, one-dimensional channel flow and steady, two-dimensional, contraction-expansion slit flow. Monodisperse and polydisperse polymers are considered, respectively. As these models predict infinite elongational viscosity, a finite chain extensibility factor is necessary to obtain physically meaningful results in uniaxial extension. A thorough investigation of Warner and Cohen nonlinear spring laws revealed that the latter law may lead to a nonphysical solution multiplicity, where two stable solutions, with a positive definite conformation tensor, arise. All the numerical results are compared with experimental observations and the predictions of Giesekus and Phan-Thien and Tanner models. Characteristic features measured experimentally in the benchmark flows are described well by all models although the tube-theory models perform, in general, more satisfactorily with respect to both the rheological data and the inhomogeneous flow data. (C) 2017 The Society of Rheology.