A new version of the tube theory based on the de Gennes-Doi-Edwards reptation concept (reported in Likhtman and McLeish's work published in 2002) is evaluated, modified to allow for simplified computations, and used to study the relationship between zero-shear viscosity and molecular weight for monodisperse entangled linear homopolymers. The Likhtman-McLeish model combines self-consistent theories for contour length fluctuations and constraint release with reptation theory for monodisperse linear polymers. Because of the nature of the Rubinstein and Colby approach used for the treatment of constraint release, the related term is probabilistic and requires stochastic simulations for the calculation of the relaxation modulus G(t). This makes the Likhtman-McLeish model computationally difficult to use. In this work we solve this problem by generating an approximate closed-form solution for the stochastic term. Then analytical integration of the relaxation modulus function G(t) provides an expression for the zero-shear viscosity (eta(0)). Results of the computations of the zero-shear viscosity and of the slope of eta(0) versus molecular weight are compared with available experimental data for monodisperse entangled linear polystyrene and polyethylene (hydrogenated polybutadiene). The model is a major improvement over previous theoretical models, even if there is still some disagreement between the predictions and experimental data of the slope of eta(0) versus molecular weight. The possibility of inferring monomer chemistry-dependent parameters from the zero-shear viscosity remains a difficult task because of the introduction of a constraint-release parameter. Nevertheless, the model is a useful tool for the prediction of linear viscoelasticity data. (C) 2004 Wiley Periodicals, Inc.