Call packing has been recognized as a routing scheme that significantly reduces the blocking probability of connection requests in a circuit-switched Clos multistage interconnection network. In this paper, for the first time, a general analytical model for the point-to-point blocking probability of the call-packing scheme applied to Clos networks is developed. By introducing a new parameter called the degree of call packing, the model can correctly estimate the blocking probability of both call-packing and random routing schemes. The model is verified by computer simulation for various size networks and traffic conditions.