Abstract: Technology for residual stress measurement by X-ray is a non-destructive testing method, which has been widely used in engineering because of the features of theoretical maturity, elegant simplicity, and high reliability. X-ray residual stress measurement is based on the elastic mechanics theory on combining the changes of crystal lattice with the elastic mechanics to calculate the residual stress. At the same time, the development of testing equipment and software has simplified the testing process, which has further aggravated the ignorance of testing principles by relevant personnel and increased the risk of the entire testing process. Based on the elastic mechanics such as Cauchy stress, Cauchy strain and Hooke's law, this paper deduces the testing formula of residual stress completely, and analyzes the calculation of the stress tensor under the plane stress and three-dimensional stress with least square method, the examples of “±ψ strain addition and subtraction method” and ellipse fitting method are given. Explained some misunderstood conceptual symbols, pointed out the problems that need to be paid attention to during the test.