Facing the machining accuracies, a methodology of identifications and tolerance design of machine tools crucial geometric error elements (CGEE) is proposed. Taking a vertical machining center as the object, the volumetric error of machine tools is modeled based on screw theory. Combined with the volumetric error model and the definitions of machining accuracies, the machining accuracies evaluation models are established, and the indirect experimental verification strategies and implementation technologies are proposed. The CGEE can be identified by orthogonal experiment and statistical analysis, and the identification results are verified by numerical experiment. Then, the mapping relationship between machining accuracies and CGEE is constructed based on response surface method, and the tolerance design of the latter is transformed into an optimization problem. Genetic algorithm is used to obtain the optimal tolerance of CGEE. While the machining accuracies meet the requirements, the product cost of machine tool is the lowest, which shows that the proposed method is conducive to the robust design of machine tools accuracies.