The influence of elasticity on peristaltic transport of Herschel-Bulkley fluid in a tube of non-uniform cross-section is investigated. The exact solutions for flow quantities such as velocity, stream function, pressure gradient, and volume flow rate are derived. The relationship between flux and pressure difference is discussed. The effects of different pertinent parameters on variation of flux along the radius of the tube are analyzed through graphs. The results show that the yield stress and fluid behavior index has significant effect on flux variation of Herschel-Bulkley fluid in a non-uniform elastic tube. The effect of elastic parameters on flux variation is analyzed. Trapping phenomenon is presented graphically to understand the physical behavior of various parameters. In the absence of non-uniform parameter the present results are similar to the observations of Vajravelu et al. [19]. © 2019 Beihang University