In this paper, an extended volumetric error model considering backlash in a three-axis machine tool was proposed and utilized for calculating the volumetric error of the machine tool at any position in three-dimensional workspace. Backlashes are interrelated; i.e. the angular backlash affects the straightness errors which then affect talc calculated squareness errors. Therefore, a new concept was introduced to define the backlash of squareness errors to incorporate the backlash of squareness error into the volumetric error, and the characteristics of the backlash of squareness error were investigated. The effects of backlash errors were assessed, by experiments. for 21 geometric errors of a machine tool. The backlash error was shown to be one of the systematic errors of a machine tool. And a generalized volumetric error model formulator for three-axis machine tools was developed, which allowed us to formulate machine tool synthesis error models far all possible machine tool configurations only with machine tool topology information. Based on these volumetric error model and model formulator, a computer-aided volumetric error analysis system was developed for a three-axis machine tool in this paper. Then the volumetric error at an arbitrary position can be obtained, and displayed in a three-dimensional graphic form.