Peristaltic transport of a non-Newtonian fluid through the annular gap between two coaxial tubes is studied. We assumed that the inner tube is rigid whereas the outer tube has sinusoidal wave travelling down its wall. We modelled the flowing fluid as a Casson fluid to study the combined effects of yield stress (plug width) and annular gap on peristaltic transport. The flow is investigated in a wave frame of reference moving with velocity of the wave under long wavelength and low Reynolds number assumption. The expressions for velocity, stream function, pressure rise, flow rate and frictional force on inner and outer wall are obtained. Results are shown graphically and discussed in the results and discussion section. It is observed that yield stress and annular gap both have significant impact on the pressure rise, frictional resistance on the walls and on the formation and variation of trapped bolus.