A method was developed for construction of mathematical models, which describe the geometry of the industrial robots and multi-axis machine tools. This method takes into account the primary deviations in size, shape and location. Primary deviations occur during manufacture of the industrial robots and multi-axis machine tools. Such deviations can be measured. For this purpose modern metrology methods may be used. A method was developed for correction of the integrated deviations in the industrial robots and multi-axis machine tools. The method allows us to offset the effect of the primary geometric deviations. The method ensures a coincidence of the trajectories of real industrial robots and multi-axis machine tools and their ideal models. The task is reduced to solving of a system of nonlinear equations. For this purpose modern numerical methods may be applied. These methods can improve the accuracy control of the industrial robots and multi-axis machine tools. Determination of the primary deviations is presented on the example of a five-axis machine tool. On the basis of a kinematic scheme of a machine tool, the following deviations were revealed. Deviation of the angular position of the spindle machine tool during its movement. Deviation from the straightness of motion along the specified axes. Deviation of the lengths of the links of the movement mechanism of the spindle. Deviations from the parallelism and perpendicularity to the axes of the turntable. Radial run out of the turntable. Axial runout of the turntable. Deviations in positioning by the linear and angular coordinates. Deviations from the parallelism and perpendicularity to the frame guides. References are made to the works of the other researchers.