An extended interchain tube pressure model for polymer melts and concentrated solutions is presented, based on the idea that the pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic (Doi and Edwards, 1986). In a tube model with variable tube diameter, chain stretch and tube diameter reduction are related, and at deformation rates larger than the inverse Rouse time tau(R), the chain is stretched and its confining tube becomes increasingly anisotropic. Tube diameter reduction leads to an interchain pressure in the lateral direction of the tube, which is proportional to the 3rd power of stretch (Marrucci and Ianniruberto, 2004). In the extended interchain tube pressure model, it is assumed that chain stretch is balanced by interchain tube pressure in the lateral direction, and by a spring force in the longitudinal direction of the tube, which is linear in stretch. The elongational viscosity data of Huang et al. (2013) are in agreement with the assumption that dilution of polystyrene by oligomeric styrene does not change the relative interchain tube pressure. Quantitative agreement between highly nonlinear viscoelastic experiments in elongation and predictions for polystyrene melts and concentrated solutions of polystyrene in oligomeric styrene is obtained based exclusively on the relaxation modulus of the polymer melt, the volume fraction of polymer in the solution and the time-temperature shift caused by the reduction of the glass transition temperature T-g of the polymer in solution relative to T-g of the melt. (C) 2014 Elsevier B.V. All rights reserved.