A low Reynolds number k-epsilon turbulence model is developed for predicting turbulent wall flows of viscoelastic fluids. The model uses a non-linear molecular viscosity that is affected by the turbulent fluctuations and a new damping function is introduced to account for near-wall effects. This new function was made equal to the eddy viscosity damping function which was derived taking into account viscometric and elastic effects.Flow predictions compare favourably with results from experiments with several viscoelastic fluids, especially the friction factor and the mean velocity. Comparisons of the turbulence kinetic energy are less good, but the model is able to capture the shift of the peak turbulence kinetic energy and rate of dissipation away from the wall, the decrease in those peak values and of the production of k, and the Reynolds shear stress deficit across the pipe. An advantage of the present single-point turbulence closure relative to previous attempts at modelling polymer drag reduction, is the fact that here the input is only the mean velocity and fluid properties and no other modifications of the turbulence model are required to deal with different fluids.Further developments of the turbulence model are suggested at the end. (C) 2003 Elsevier B.V. All rights reserved.