In this research, a technique was developed for quantitatively evaluating the amount and distribution of tensile and compressive residual stresses by the combined use of strain measurements under the spherical indentation loading together with the finite element method (FEM). When the spherical indentation is applied to the top surface of a welded plate, the elastic strain at an optimized position near the indentation is measured by strain gauges, where the residual and applied indentation stresses are largely superposed. In order to analyze the residual stresses, FEM analysis was conducted to establish the relationship between the elastic strain adjacent to the indentation and the indentation pressure for plates subjected to various uniform tensile and compressive stresses. The critical indentation load was identified, which maximizes the difference between the tensile and compressive residual stresses. A strain energy term (U*) is newly introduced by integrating along the trajectory between the indentation pressure and the elastic strain in a range from 0 to maximum pressure. The application of this technique could contribute to improved reliability in welded parts.