Abstract: Residual stress will inevitably be introduced during the manufacture of mechanical components and products. Residual stress has an important impact on component performance and service life. There are many methods for testing residual stress. As a nondestructive testing method, X-ray testing technology has been widely used in engineering due to its mature theory and simple method. The characterization of residual stress is analyzed, and several confusing concepts in the definition and characterization of residual stress are further explained from the perspective of elastic mechanics; the conditions of linear fitting and ellipse fitting are analyzed.