Abstract: In the implementation of the National Standard for Form and Position Tolerances an Important task is the accurate measurement of form and position errors. Presently, roundness measuring instruments are available while special instruments for measuring cylindricity and coaxality are non-existent. Measuring instruments equipped with data processing facilities are rare. This paper presents the}principles for measuring roundness, cylindricity and coaxality as well as the analytical method for linear data processing on computer. These will be helpful to the design of new special measuring instruments. In comparison with the general purpose instruments, these new equipments might improve the accuracy and efficiency of .measurement. Due to the fact that roundness measurement with data processing is the foundation of the above-mentioned three items of measurements, this paper thus lay main emphasis on the introduction of measurement and data processing of roundness; meantime the requirements for setting up of the measured parts are presented also.