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The velocity distribution of particles flowing in a two-dimensional mass-flow hopper under gravity was obtained for the entire region of a hopper by measuring the position of tracer particles against time. The characteristic regions of discontinuity or rapid change in velocity and flow direction were found from a detailed analysis of the velocity distribution obtained. On the other hand, an approximate calculus for the estimation of the “velocity characteristic curve” and “stress characteristic curve” (i.e., slip line) was proposed on the basis of the plasticity theory. Theoretically, discontinuity in velocity is possible across the velocity characteristic curve. It was confirmed that both the characteristic regions estimated and obtained experimentally were identical Also, it was confirmed that the slip lines appear in the flow field that developed immediately after the yield of material occurred.† This report was originally printed in KAGAKU KOGAKU RONBUNSHU, 13(3), 340-347 (1987) in Japanese, before being translated into English by KONA Editorial Committee with the permission of the editorial committee of the Soc. Chemical Engineers, Japan.