Current networks are multi-service packet-switched environments, very often based on Internet Protocol, where the provision of good quality services is a great challenge. The most popular service, offered by almost every network, is voice transmission. As a real-time service, it places high demands on bandwidth and delay. The paper describes selected network dimensioning problems for the voice over IP service. The authors discuss service quality measures in legacy circuit switched networks and the key performance indicators that influence the quality of telephone service in packet networks. The main contribution of the paper is the proposal of utilizing the blocking probability calculation, which is based on the B-Erlang model used in legacy systems, to estimate the average bandwidth needed to handle a number of sources generating voice traffic in IP networks. Taking into account the average bandwidth required to carry out a one voice conversation, the total network capacity was calculated. The authors made analytical calculations which were confirmed by simulation studies. The problem of using different codecs and their influence on bandwidth consumption and overall service quality experienced by a user were also discussed in the paper. At the end of the paper, the authors defined the directions of further research that should be carried out, i.e. the development of dimensioning methods for networks carrying multimedia services with particular attention paid to video transmission and reliable quality assessment.