The work aims to propose a multi-person congestion model based on Markov, in order to reduce the congestion rate of the picking system and improve the transportation efficiency of emergency materials. The Markov state transition matrices of single picking in cargo slot and multiple picking in cargo slot in narrow channel were constructed to solve the stationary distribution, and obtain the functional relationship between the picking probability and the congestion rate. The effect of different factors on the congestion rate was analyzed by simulation. Under single picking in cargo slot, the system congestion rate reached its peak at the picking probability of about 0.3, and then decreased with the increase of the picking probability. Under multiple picking in cargo slot, the picking probability was positively correlated with the system congestion rate, and the system congestion rate increased with the increasing picking probability. Therefore, in the actual picking operation, in order to reduce the system congestion rate, the picking probability of about 0.3 should be avoided under single picking in cargo slot and under multiple picking, the picking probability should be reduced as much as possible.