Peristaltic pumping of fluid is a fundamental method of transport in many biological
processes. In some instances, particles of appreciable size are transported along with the
fluid, such as ovum transport in the oviduct or kidney stones in the ureter. In some of
these biological settings, the fluid may be viscoelastic. In such a case, a nonlinear
constitutive equation to describe the evolution of the viscoelastic contribution to the
stress tensor must be included in the governing equations. Here we use an immersed
boundary framework to study peristaltic transport of a macroscopic solid particle in a
viscoelastic fluid governed by a Navier-Stokes/Oldroyd-B model. Numerical simulations of
peristaltic pumping as a function of Weissenberg number are presented. We examine the
spatial and temporal evolution of the polymer stress field, and also find that the
viscoelasticity of the fluid does hamper the overall transport of the particle in the
direction of the wave.