Usual application of a transmision line system requires that impedance of the line is matched to the load with the aid of one or two tuning stubes. The conventional practice of trasmission line system design employing the Smith chart, a well-known transmission line chart, was studied as a guide to set up algorithms for computer programming. The current research investigates the construction and application of the Smith chart. The chart was mathematically analyzed to determine the relationship between the electrical impedance and the coordinates on a complex plane. In moving a specific point to another required points on a transmission line or coresponding point on the Smith chart, the required point may be specified by any of the following : 1) a given distance in a particular direction, 2) a given per unit resistance, and 3) a given per unit reactance. For each alternative specification of the required point, equations and algorithms were derived to obtain the coresponding coordinates in a complex plane. To facilitate computerization of single-and double-stub tuning on a transmission line system, spacing-circle equation was found and algorithm for calculation of admittance at the stub location was derived. As a result, stub length(s) could be easily obtained. The software was developed in Pascal language and capable of aiding in the design of a transmission line system, displaying computing results in graphic display mode, and allowing users to make a hard copy on to the printer. The software was tested with a few design examples of known solution and test results are included in this report. The test results have shown that the software performance is satifactory and is as required by the software specifications.