This paper presents a new approximate recurrent calculation method of the blocking probability in a switching node of virtual circuit networks which is offered a mixture of different traffic streams, including multicast traffic streams, generated by a finite population of two-state sources. The method is based on transforming a multi-dimensional service process in the system into a one-dimensional Markov chain. The basis of the proposed calculation algorithm is an assumption about equality of reverse transition rates in both infinite and finite population models. Such an assumption allows us to determine the number of idle sources of particular traffic classes, which consequently leads to determination of offered traffic load in particular states of the group occupancy. Analytical results of the blocking probabilities in exemplary switching nodes are compared with simulation results.