In bin/hoppers filled with densely packed hulk materials, upon opening of the outlet, a narrow plug-type flow zone propagates upward and widens. With progressing discharge, this zone grows, eventually reaching the top of the material and possibly the walls of the bin. Based on small-scale model tests, a theoretical model of the evolution of the plug flow zone in plane and axisymmetric bin/hoppers is presented. The model is purely kinematic and approximate; however, it accounts for the observed lower than initial density of the flowing material, and the general form of the flow pattern. This is accomplished by separating flow into two regions, radial and vertical, separated from the stagnant material by density shocks. Comparison between the model and plane flow experiments shows satisfactory agreement providing additional assumptions relating the radial and vertical flow are introduced. The model may find application in predicting transition from plug to mass flow.