The optimal routeing problem of maximizing system throughput in series-parallel networks with finite buffers is studied in this paper. The problem is extremely difficult to solve since closed form expressions are not easily constructed for throughput in finite networks. A piece-wise linear upper bound on the throughput of a tandem network is used to develop a throughput approximation in seriesparallel networks. Based on this approximation we are able to specify a suboptimal range for routeing probabilities at each junction in the network as a function of the arrival rate to this junction. We also specify a unique value for the routeing probability at each junction, independent of the arrival rate to that junction. We then construct an O(N) algorithm to analyse general series-parallel networks with more than one junction and specify the sub-optimal routeing probabilities at each junction.