Machine tools usually cut two or more surfaces after the work piece clamped on work table. In order to improve the machining accuracy and optimize accuracy design, it is hoped that the geometric errors that influence the accuracy of machined surface prominently can be known beforehand, so the adjustment will be carried out with a definite objective rather than without any clue. Because the machining accuracy of each direction in 3-D space is different value, in this paper, machining accuracy failure mode was defined as the various combination of the machining accuracy of each direction according to whether it is up to the reserved objective value or not. A three-axis machine tool was selected as an example and there were 7 machining accuracy failure modes for it. Based on the generalized correlation analysis, the correlation relationships between 7 machining accuracy failure modes were analyzed, and the main failure modes that affect the machining accuracy of work piece to be machined were identified. For each machining accuracy failure mode, key geometric error that had major influence on it was identified based on sensitivity analysis. Finally, four stepped work pieces were milled by a 3-axis machine tool to illustrate the analytical method proposed in this study.