In this paper we investigate the yield condition in the mobilization of yield-stress materials in distensible tubes. We discuss the two possibilities for modeling the yield-stress materials prior to yield: solid-like materials and highly-viscous fluids and identify the logical consequences of these two approaches on the yield condition. Our results reveal that these two modeling approaches have far reaching consequences on the yield bottleneck and hence should be critically examined in the light of experimental evidence. As part of this investigation we derive an analytical expression for the pressure field inside a distensible tube with a Newtonian flow using a one-dimensional Navier-Stokes flow model in conjunction with a pressurearea constitutive relation based on elastic tube wall characteristics. This analytical expression has wider applicability than in the identification of the yield condition of yield-stress material.