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In order to improve the accuracy of NC machine tool and reduce the influence of geometric errors caused by assembly and manufacturing process, the geometric error model was established based on multi-body system theory, and a new method of identifying key elements of the geometric errors was proposed on the basis of geometric errors correlation analysis. Firstly, geometric errors model of three-axis vertical CNC machine tools was derivated by using multibody system theory and homogeneous coordinate transformation method, and correlation analysis model of the geometric error elements was established, which contained 21 geometric errors of three-axis NC machine tools. Secondly, to avoid the defects of single factor analysis, and considering the coupling effects of geometric error elements, Latin hypercube sampling method was used in the whole parameter space sampling. Finally, based on the geometric error model and correlation analysis model, spatial error was calculated by using geometric errors element which was determined by Latin cube sample. And the key geometric error elements that affected the accuracy of machine tool were analyzed. Before error compensation, the twelve-line method was applied to identify the geometric error elements for each axis based on Renishaw XL—80 laser interferometer measuring system. The comparison result of circular tests after error compensation showed that the method can effectively and quantificationally identify the key factors that affecting the precision of machine tool space and the effects of error elements of total space error, thus important theoretical foundation was provided for accuracy allocation and error compensation of machine tool reasonably.