We consider a cyclic flow line model that repetitively produces multiple items in a cyclic order. We examine performance of stochastic cyclic flow line models with finite buffers of which processing times have exponential or phase-type distributions. We develop an exact method for computing a two-station model by making use of the matrix geometric structure of the associated Markov chain. We present a computationally tractable approximate performance computing method that decomposes the line model into a number of two-station submodels and parameterizing the submodels by propagating the starvation and blocking probabilities through the adjacent submodels. We discuss performance characteristics including comparison with random order processing and effects of the job variation and the job processing sequence. We also report the accuracy of our proposed method.