A phenomenological model has been developed to predict the time-dependent flow behavior of a suspension of solid particles in viscoelastic fluid. The model consists of a Maxwell model in parallel with a plastic model, which has a yield stress parameter Y. The effect of the solid particles is studied by introducing a function f(Ï†), where Ï† is the volume fraction of the solid in the viscoelastic fluid. Einstein's, Mooney's and Simha's models, which are good for suspensions of rigid spheres in Newtonian fluids, are used for f(t) to examine the effect of <> on the velocity profiles in tube flow. The volume fraction was varied from 0 to 307. An explicit finite difference method is used to solve the integrodifferential equation for viscosities up to 5.0 poise, and relaxation times between 1 and 5 seconds. Pressure drops are calculated using the average velocity obtained from the computed velocity profiles. Limitations of the numerical method and the simple rheological model are discussed and recommendations for the future have been made.