Abstract Through analyzing the stress state and deformation of pipe bending using local induction heating with small bending radius, a computer simulation system has been developed based on the FEM software ANSYS and finite strain elasto–plastic theory. The results, such as the thinning and thickening ratio of the pipe wall thickness, the pushing force with or without a reverse moment acting on the bending arm, the proper reverse moment that is to be applied on the bending arm to control the wall thinning ratio of the bending outside to within a particular value, the ovality of the cross-section of the pipe and the spring-back angle after unloading and so on, can be obtained using this system. Pipe-bending process with a relative bending radius R/D0=1.5 and with or without a reverse moment acting on the bending arm has been simulated.