This report describes the use of computer techniques for analysing the alignment sensitivity of propeller shafts and calculating the optimum alignment. It goes on to describe how to achieve the calculated alignment on a ship, and to make use of the results of the computer analysis. The practical applications are illustrated by means of a case study. Some investigations into the changes in shape of the ship which occur for different conditions of loading and the influence of these shape changes on shaft alignment are describes in an Appendix.