We propose an approximation method for sojourn time distributions in telecommunication networks consisting of general queuing networks. The queuing network is of the open network type, and has n single server queuing systems with arbitrary interconnections. Customers may enter the network at any queuing system. The interarrival times of the external arrival processes and the service times at the queuing systems are generally distributed. The analysis is based on the methods of decomposition, two-moment approximation, waiting time approximation and semi-Markov chain construction. All related processes are approximated by the first two moments only. Numerical results are compared with simulation ones in order to validate the proposed method.