“…1 shows the time development curve of the front of slump flow tests with almost constant yield stress conducted by Kokado, et al 3), 4) . As pointed out by Hosoda, et al 2) , it is worth to note that the time development curves lean towards an asymptotic curve, which is characterized by 1/1 slope with the decrease of plastic viscosity. Following such observation, our motive in this study it to derive such asymptotic curve in the limit of low plastic viscosity, for a problem set in Cartesian coordinate system, which will be our first step towards obtaining a theoretical curve capable of describing the time development of the front of slump flow for a practical range of and values in the near future.…”