[23] analyzed the relationship between the energy required in the indentation process and the residual stresses according to the principle of the conservation of energy from the perspective of the work done by residual stress, and derived a more simple formula for calculating residual stress. In the Vickers indentation cycle, the stress type and its value can be easily calculated using the energy method without any comparison of the load-displacement curve of the non-stressed reference material. [PERSON] et al. [24] proposed a method to measure the value of the residual principal stress component by measuring the deposition height in different directions of the indentation. The assumption made by the model was that there is a linear connection between the residual stress and the highest load when compared to specimens without any stress. Stress-induced load displacements lead to micromechanical contact. The value of the stresses calculated from the contact analysis is nearly of the same magnitude as the stresses applied in the plane. However, when the stresses applied are pure shear stresses, the effect of in-plane stresses on the plastic deformation of the indentation is negligible. Different stress components of the residual stresses result in different deposition heights of the sample along the main direction. The deposition height can be obtained by performing optical microscopy tests on the indentation. However, the disadvantages of this method are also obvious, it is difficult to accurately measure the height of accumulation and it consumes too much time with related work. With the continuous development of indentation technology, the indentation method has been widely used in various fields, but it still has disadvantages. If the relationship between residual stress and hardness can be established, using hardness to evaluate the residual stress of materials will help in obtaining a stress measurement and in the monitoring of in-service equipment, so it is necessary to conduct more in-depth research on residual stress measurement by the indentation method. When the indentation method is applied to measure hardness, the surface residual stress will affect the shape and size of the indentation. In indentation experiments for workpiece surface without residual stresses, the purely elastic deformation of elastoplastic prismatic indentations was transformed into plastic yielding when the average pressure in the contact zone increased above its yield stress. Hydrostatic stresses are known to have no effect on the plastic deformation of an indentation. Biaxial compressive residual stresses lead to an increase in the critical mean contact pressure at yielding. Biaxial tensile residual stresses reduce the critical mean contact pressure at yielding. A similar residual stress effect exists in the transition phase from elastic to plastic deformation. When the average contact pressure reaches a maximum value, the indentation deformation transforms into the fully plastic phase. As shown in Figure 1, the hardness of a material increases as the applied compressive residual stress increases. The higher the compressive residual stress, the sooner the indentation changes to a fully plastic state. On the contrary, the higher the tensile residual stress, the lower the hardness of the material and the deeper the indentation needed to obtain a fully plastic state. With the same indenter, the deeper the indentation depth \(h\), the larger the projected surface area of the indentation. In view of this, this study proposed a method to determine the quantitative relationship of hardness with residual stresses by examining the indentation area, and obtained residual stress indirectly through measurements of the micro-hardness of a machined surface. In this study, a theoretical model of positive rhomboid indentation with equal biaxial residual stress was established. Then, the model was modeled by the finite element method.