The paper investigates the nanoindentation process with different rates in the Cu (001) of FCC system. The indentation process was done using molecular dynamics simulation based on the embedded atom method theory and Morse potential. Simulation process of indentation used a rigid spherical indenter with the diamond structure. To structure characterization we applied the adaptive common neighbour and the dislocation extraction analysis. It was found that the range of the linear change of the indentation force depends on the rate of response of the system. The initial range of the linear dependence of stress evolution also depends on the rate of indentation. Moreover, the average total normal stress in the system is only compressive. After linear changes, we observe oscillating changes in stress evolution. During indentation, for the range of linear changes of stress, dislocations aggregated only around the indenter surface. The creation of dislocations is directly connected with the structural changes. The structure analysis revealed the formation of HCP and BCC structure in the Cu (001) of FCC systems and a correlation with the creation of dislocations.