This thesis is the summary of the research work that has been carried out by the author on the development of methods of optimum gear design and shaft design for gear boxes, and the integration of the methods into one software package together with parametric layout drawing. The objective of the optimum gear design is to minimise the gear centre distance with a fixed aspect ratio of pinion, when power capacity requirement is given. Although power capacity is dependant upon many factors, the optimum gear design method has used module, numbers of teeth, and helix angle as the significant variables. The power capacity rating is calculated by AGMA standards and the optimum design method is based on a study of the numerical behaviour of the AGMA power capacity rating and transformation of the gear design constraints into direct limiting boundaries on design variables. Numerical example tests show that the method is efficient and effective in finding the global minimum centre distance design. The shaft component design method is based on established theories for reaction calculation, bearing life rating, shaft stress calculation and shaft failure criterion. However, the layout of the gear box is defined by a unique system using vectors connecting shaft and gear centres. The gear design and shaft design methods are implemented in an integrated software package and a well defined data organisation provides the basis for data sharing. The definition of layout by centre vectors also serves as the reference frame around which to draw the layout by parametric programs. The design results of the software package are obtained by parametric programs from a data file based on the same data organisation. Parametric programs for individual shaft, bearing, and gears are written to draw the components and main dimensions such as centre distances, component axial positions, gear sizes and bearing sizes are shown on the layout. The contribution to knowledge by this investigation is mainly in the gear design area, viz., the study of the numerical behaviour of AGMA standards in relation to gear geometry and the development of the efficient and effective algorithm for the optimum gear design. The descriptive layout definition by centre vectors is also a novel feature.