To quantify and identify the crucial geometric errors which constrain machine accuracy in the process of manufacturing and fabricating parts, we introduced Jacobian-torsor model to study the geometric error of dual-drive z-axis assembly in horizontal machine center. Combined the tolerance zone of parallelism and straightness, we determined the variation range and constraint equation of torsors based on dimension and geometric tolerance, and then we established the error model. We compared the simulation results and the measured error data of similar conditions, and used Sobol sensitivity analysis method to identify crucial geometric errors. The results show the availability of the Jacobian-torsor model in geometric error analysis quantificationally. The lead error of ball screw, flatness of base, straightness of guide and parallelism between sliders in Y direction were identified as the crucial errors, and the intercoupling of some errors is obvious.