The present article proposes a new method for modelling multi-service packet networks with implemented traffic overflow mechanisms. The basis for the proposed method is a special convolution algorithm that enables to determine the occupancy distribution and the blocking probability in network systems in which packet streams (calls) of individual traffic classes can be serviced by both direct and alternative resources. The algorithm worked out by the authors makes it possible to model systems with any type of traffic offered to direct groups. The methods that are to be found and are described in the literature of the subject permit the researcher to model systems in which direct groups are offered either Erlang or Engset streams.