A novel way of continuous surface hardening of steel bodies by a laser beam is modeled. This heat treatment is supplemented with pre-heating of the hardened parts by a classic inductor in order to reduce the temperature gradients and subsequent mechanical stresses in the processed material. The mathematical model of the process is solved numerically in 3D and the solution respects all important nonlinearities (a saturation curve of the hardened steel and temperature dependences of its physical properties). The methodology is illustrated with a typical example, whose results are presented and discussed
