An approximation algorithm is presented for cyclic queueing networks with finite buffers. The algorithm decomposes the queueing network into individual queues with revised arrival and service process and revised queue capacity. Then, each queue is analyzed in isolation. The service process reflects the additional delay a unit might undergo due to blocking and the arrival process is described by a 2-phases Coxian ($C_2$) distribution. The individual queues are modelled as $C_2/C_2$/1/B queues. The parameters of the individual queues are computed approximately using an iterative scheme. The population constraint of the closed network is taken into account by ensuring that the sum of the average queue lengths of the individual queues is equal to the number of customers of the network. Extensive numerical experiments show that this method provides a fairly good estimation of the throughput.