The optimal buffer allocation in queueing network systems is a difficult stochastic, non-linear, integer mathematical programming problem. Moreover, the objective function, the constraints or both are usually not available in closed form, making the problem even harder. A good approximation for the performance measures is thus essential for a successful buffer allocation algorithm. A recently published two-moment approximation formula to obtain the optimal buffer allocation in general service time single queues is examined in detail, based on which a new algorithm is proposed for the buffer allocation in single-server general service time queueing networks. Computational results and simulation results are shown to evaluate the efficacy of the approach in generating optimal buffer allocation patterns.