The paper discusses a methodology for simulating friction stir processing in order to determine the process parameters and to provide surface hardening for flanges with a cavity. In accordance with the developed methodology presented by the results of literature analysis, it describes a computational computer model developed in Ansys Mechanical and based on the finite element method. The thermophysical properties of the material under study and the tool material, which are taken into account in the FEM simulation of the processes, are presented as dependent on temperature. By comparison with experimental research, the simulation results are verified in terms of a number of parameters, such as the depth of the hardened layer and the diameter of the surface area of the faces of holes for bolted joints. The results of measuring the microhardness of the hardened layers of the AISI 420 steel are presented, and their dependence on the depth of the hardened layer is determined. Numerical simulation is used to compute the values of the geometrical parameters of the areas subjected to surface hardening by friction stir processing with the variation of the process parameter, namely tool rotation speed, the force acting along the normal to the surface being processed, and the friction coefficient. The numerical simulation gives results on the thermal state of the specimen, particularly, maximum temperatures in the contact zone, as well as temperature and time dependences.