This study reports computer predictions of the thermo-mechanical behavior and residual stresses during the quenching process of the notched cylinder of steel material with local rapid heating by induction method. The computer simulation is based on the metallo-thermo-mechanical theory and finite element analysis coupled temperature. phase transformation and stress/strain fields. From this research, we can know that the compression residual stresses with a large level be formed on the surface of the part by using quenching with induction heating process.