Abstract: Since the late 1980s, one trend of research on processor arrays is to design linear processor arrays. Lee and Kedem did the pioneer’s work in this field as they proposed a framework for designing linear arrays. Their framework consists of three parts: the first part is a linear array model; the second part uses pairs （ H, S ）, where H and S are vectors, to denote designs; and the third part is a group of necessary and sufficient conditions for pairs （ H, S ）. Thus far, there are no practical design methodologies proposed in the literature. In the paper here, a design methodology is presented for three dimensional algorithms. This methodology is based on two observations: first, given a three dimensional algorithm, designers can directly determine several feasible pairs （ H, S ） by analyzing the longest path of the dependence graph （DG） of the algorithms; second, if the longest path satisfies a certain condition, one of these pairs （ H, S ） is computation time optimal. In summary, this methodology can produce computation time optimal design for some three dimensional algorithms. Finally, the matrix multiplication and the transitive closure problem are taken as examples to illustrate the application of the methodology.