X射线残余应力测试是基于弹性力学理论，通过X射线衍射测量材料晶格变化，并和弹性力学相结合来计算材料的残余应力的。现行标准GB/T 7704-2017《无损检测X射线应力测定方法》中对于残余应力测试的计算部分的表述较为简略，增加了试验人员对标准理解的难度。同时检测设备和软件的发展使得测试过程变得简单化，也进一步加剧了相关人员对测试原理的忽略，增加了整个测试过程的风险。从柯西应力、柯西应变、胡克定律等弹性力学定律出发，较为完整地推导了残余应力测试的公式，详细分析了最小二乘法计算平面应力与三维应力状态下的应力张量的原理，给出了“±ψ角应变加减法”与椭圆拟合法的示例，解释了一些容易误解的概念符号，指出了在测试过程中需要注意的问题。

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.