Abstract. When the laser intensity becomes higher than 10 22 W/cm 2 , the motion of an electron becomes relativistic, and emits large amounts of radiation. This radiation energy loss transferred to the kinetic energy loss of the electron, is treated as an external force, the "radiation reaction force". We show the new equation of motion including this radiation reaction and the simulation method, as well as results of single electron system or dual electrons system with Liénard-Wiechert field interaction.