The 3D finite element simulations are conducted for the cold working of a fastener hole in a low carbon steel plate. The simulation models the actual cold working process where the hole edge is chamfered with die-press. The agreement of finite element method and experimental results is good enough. The residual stresses are analyzed under the different die-press parameters and contact conditions i.e. die-pressing depth, friction factor, the die taper. The main results in this work are as follows: With increasing in chamfer depth the maximum compressive residual stress shows an increasing within the chamfer range of C1.5; the compressive residual stress is decrease with increasing friction; with increase in die taper the maximum compressive residual stress shows the slow increase. The efficiency for enhancing the load-carrying capacity of structural components with cylindrical holes subjected to bending load has been proved by means of FE simulation. The study shows that the simulations of cold working are necessary for if predicted residual stresses are to be used to assess fatigue life and for design die-pressing tool, improvement of parameters of the process of DP working.