Recently as electronics and semi-conductor industry develop, ultra-precision machine tools that use air-spindle with externally pressurized air bearing appear in need of ultra-precision products which demand high precision property. Effects of air compressibility absorbs the vibration of shaft, this is called averaging effect, however, the higher running accuracy is demanded by degrees, the more important factor is machining errors that affect running accuracy of shaft. Actually, it would be very important in the view points of running accuracy to understand effects of machining errors on the running accuracy of the spindle system quantitatively to design and manufacture precision spindle system in the aspect that efficiency in manufacturing spindle system and performance in operation. So fu, there are some researches on the effects that machining error affect running accuracy. However, because these researches deal with one bearing of spindle system, these results aren't enough to explain how much machining errors affect running accuracy in the typical spindle system overall. In this study, we investigate the effects of the perpendicularity error of bearing and shaft on running accuracy of spindle system that consists of journal and thrust bearing theoretically, and suggest design guideline about shape tolerances.