An expert system is developed which can design the power transmission involute cylindrical gears on the basis of strength and durability. Bending strength, surface durability, scoring, and wear probability are considered as the basis. The basic components of the expert system are knowledge base, inference engine, and working memory. The knowledges in knowledge base are classified hierarchically into the knowledges used in selection of gear type, selection of materials, and determination of K factor and are represented by rules. In the inference engine two inference methods are implemented with the depth first search method. For-ward chaining method is introduced in the selection of gear type and materials and in the determination of K factor. Backward chaining method is introduced in the detailed design of module and face width in accordance with the validation of strength. And inference efficiency is achieved by constructing the part needing a lot of numerical calculations in strength estimation separately from inference mechanism. The working memory is established to save the results during inference temporarily. In addition, design database of past design results is built for consultation during design and knowledge acquisition facility, explanation facility, and user interface are included for the usefulness of user. This expert system is written with the PROLOG programming language and the FORTRAN language in numerical calculation part which interfaced with PROLOG and can also be executed on IBM-PC compatible computer operated by MS-DOS alone.