In this paper, we introduce tree types of switching networks, I, e., a fully segregated type, a partially integrated type, and a fully integrated type switch, to accommodate nx 64Kb/s multi-slot connection traffic and analyze their blocking probabilites for the different traffic mixes by utilizing a computational algorithm of blocking probability, and finally determine the traffic handling capacity which satisfies the given grade of service. The fully integrated type switch can accommodate the ISDN traffic with relatively low wideband traffic. However, either the partially integrated type or the fully segregated type switch is needed to accommodate the ISDN traffic as the wideband traffic increases. This result can be usilized in the design of ISDN switching networks accommodating multi-slot connection traffic.