Abstract This paper presents a systematic computation algorithm for the analysis of one-dimensional, constrained distributed parameter systems. The methodology is based on the transfer function approach in frequency domain and gives exact closed-form solutions for both the free and forced responses. It is shown that eigenfunctions can be evaluated in a straight-forward manner and only algebraic manipulations are involved. The algorithm is shown to be useful for both symbolic and numeric computations. The vibration analyses of a non-uniform four-span beam and a coupled rotating shaft system are considered using the proposed computation scheme. The programming structures for both problems are the same which demonstrates the versatility of the algorithm. In addition, since the algorithm takes advantage of symbolic programming, the programs for both vibration problems are straight-forward and simple.