In this paper bandwidth reservation algorithms for a virtual circuit switching node are proposed. The node is offered a mixture of different multi-rate traffic streams, including multicast streams. An analytical method of blocking probability calculation in the considered system is also proposed. It is assumed that each of outgoing directions of the node could be modelled by a limited-availability group composed of links of various capacities. Hence, the model enables calculations of blocking probabilities for calls of all traffic classes for any structure of the groups forming the outgoing directions. The problem of blocking probability evaluation in the switching node with bandwidth reservation and multicast connections is solved in the paper by the fixed point methodology. Analytical results of the blocking probabilities in a switching node with bandwidth reservation are compared with simulation results. This research indicates a high accuracy of the proposed model.