In this work, we have numerically studied the effect of a fluid's yield stress on the single-species flow driven by large-amplitude peristaltic waves propagating with different phase shifts along the upper and/or lower walls of a closed cavity. A multiple-relaxation-time, Lattice Boltzmann code was developed for studying the effect of the Bingham number on the flow kinematics having assumed that the viscoplastic fluid of interest can be represented by the bi-viscous model. Numerical results show that the Bingham number has a strong effect on the flow kinematics with its severity being dependent on the parameters of the travelling wave. The Bingham number was also found to strongly affect the drift parameter a measure of the mixing efficiency within the channel. It is concluded that, when dealing with the flow of viscoplastic fluids in a microchannel, it is better to go for large-amplitude asymmetric peristaltic waves if mixing enhancement is desired. For symmetric waves, it is possible for the drift parameter of Bingham fluids to be larger than that of Newtonian fluids provided that the wavenumber is sufficiently large and its amplitude is sufficiently small. And, when the amplitude ratio is small, it is better to work at small Womersley numbers in order to have a larger drift parameter. (C) 2017 Elsevier B.V. All rights reserved.