Abstract—In machining operations, the rigidity of the machine-tool-workpiece system is one of the main criteria that have high influence the process capability in terms of part accuracy and process precision. In this study, a special mathematical model was developed for predicting the profile error received on a cylindrical part during turning operation as a result of variation in machine-tool rigidity during the feed movement of the lathe cutting tool. A graphical presentation of error formation caused by elastic squeezing of shaft sections under the action of the cutting force is generated in this work. The study can present a guide for engineers and technical interested in determining the error expected during machining of precise shafts and other long mechanical components having relatively low stiffness.