We present analytical solutions for fully developed pipe and channel flows of two viscoelastic fluids possessing a Newtonian solvent, where the polymer contribution is either described by the Phan-Thien-Tanner (PTT) or FENE-P models. We derive in detail the pipe flow solution for the PTT fluid, and present the final solutions for the remaining three cases. This constitutes an important addition to existing results where the presence of a solvent with Newtonian characteristics has been consistently overlooked, as it posed considerable difficulties to the task of obtaining a closed form solution. In addition, interesting aspects of the solutions are discussed. (c) 2005 Elsevier B.V. All rights reserved.