A novel methodology has been presented to build a synthetic volumetric error model of a multi-axis NC machine tool of arbitrary configuration. The model includes original position errors and motion errors that account for geometric errors owing to manufacture, installation and motion control inaccuracy, thermal errors from thermal deformation of tool, machine and workpiece and mechanical loading errors etc. Thus it describes the error's facts of a machine tool and is useful to real-time compensation of the overall errors within the machine's working volume specially. In order to develop the new model, multi-axis kinematics and homogeneous transform matrices are utilized. Finally, based on the proposed modeling theory and method, the error model of a 3-axis NC vertical machine tool is introduced. In addition, its 36 error components are analyzed.