<p>Prediction of residual stresses in machining is significant for high performance machining. In previous work the analytical model of residual stress was based on the cutting mechanism, but the stress relaxation procedure is difficult to understand and solve. A modified relaxation-free algorithm is proposed based on inclusion theory, revealing that the essence of residual stress is influenced by plastic strain. For the first time, thermal stress and temperature are considered in the inclusion theory. Mechanical stress, thermal stress models and Sehitoglu-Jiang relaxation algorithm are introduced. And a relaxation-free method based on inclusion theory is proposed; the equivalence of two methods is proved in detail. The simulation results show that the proposed method is equivalent of an analytical model which uses S-J as the error is less than 10 %.</p>