Machining-induced residual stresses can significantly influence the performance of machined parts, and many scholars have contributed efforts to measure, evaluate, predict, and control the distribution of residual stresses. In most published researches, the residual stresses are analyzed as the function of cutting parameters, tool parameters, or material properties, but any of these parameters cannot decide the distribution of residual stresses solo and directly. And the commonly used evaluation criteria, like surface value, peak value, and existing range, cannot reflect the overall distribution of residual stresses. In this paper, a new approach to study this issue was proposed, and the cutting loads, the cutting parameters, and the evaluation of residual stress field were unified to the concept of energy and its mutual transformation with mechanical work. The effective cutting power on the machined surface was analyzed, and the integral of strain energy density over depth and the power of stored strain energy were supposed to be the energy criteria of residual stress field. Face milling experiments were carried out, and the cutting forces and the in-depth residual stress distribution were measured. According to the methodology proposed, the results showed that with the increase of effective cutting power, the power of stored strain energy increases with growing rate, which means that the partition of cutting work stored as strain energy increases simultaneously. And the integral of strain energy density over depth grows linearly with the effective cutting power under the experimental conditions in this study.