Abstract: It is well-known that the productivity of Flow-Shop systems is not only related with the number of parts pallets, but also with the capacity of machine buffers. How, ever, up to now there is not any practical approach for quantitative description for the buffer of Flow-Shop systems. In this paper, to both 2xn systems and mxn systems we present an estimation of the upper bound of the capacity of minimal buffer of each machine and bottle neck machine can be utilized sufficiently. This result provides us some theoretical basis for both increasing the productivity of Flow-Shop systems and optimizing the system design.