At the Kielce University of Technology a new concept of accurate measurements of sphericity deviations of machine parts has been developed. The concept is based upon measurement of roundness profiles in many clearly defined cross-sections of the workpiece. Measurements are performed with the use of typical radial measuring instrument equipped with a unit allowing accurate positioning of the ball. The developed concept required finding a solution to numerous problems relating to the principle of the radial measurement. One of the problems to be solved was matching of measured roundness profiles. The paper presents an outline of the developed concept of sphericity measurement, a mathematical model of profile matching and results of the verification of the model.