Using a circulating fluidized bed (CFB) as a typical column-type solid/gas system, this study aimed to determine the minimum gas velocities restraining the downward-flowing particles through the contraction midway of the CFB riser, and to formulate an algebraic expression of these critical velocities. Using glass-beads as circulating particles, change in the amount of downward-flowing particles at the contraction with change in gas velocity was examined experimentally for different solid feeding rates. Algebraic expression of critical velocities was performed with a growing chain model (GCM) and a revised GCM (RGCM). The GCM proposed by us and others is an ideal cluster model that assumes a vertical chain of particles of a constant size. The RGCM further takes account of the size distribution of circulating particles. The experimental results with circulating particles of different size ranges of 125-280, 90-225 and 28-90 mum revealed that the critical gas velocities are proportional to the solid feeding rates, and the slopes of those curves are almost the same, irrespective of the size distribution of circulating particles. The critical velocities obtained by extrapolating the curves of experimental critical velocity towards zero of solid feeding rate showed a linear relations with the theoretical terminal gas velocities of an infinitely long chain of particles given by the GCM and RGCM. From this, the critical velocity can be presented as a linear expression of the solid feeding rate and the theoretical terminal gas velocity of an infinitely long chain of particles. The theoretical expression of the critical velocity using the theoretical terminal gas velocity of an infinitely long chain of particles by the RGCM is confirmed to be adequate, since this expression can also predict experimental critical velocities for 28-280 mum circulating particles with an error of only +/-10%.