Molecular dynamics simulations are performed to investigate the influence of irradiation damage on the mechanical properties of copper. In the simulation, the energy of primary knocked-on atoms (PKAs) ranges from 1 to 10 keV, and the results indicate that the number of point defects (vacancies and interstitials) increases linearly with the PKA energy. We choose three kinds of simulation samples: un-irradiated and irradiated samples, and comparison samples. The un-irradiated samples are defect-free, while irradiation induces vacancies and interstitials in the irradiated samples. It is found that due to the presence of the irradiation-induced defects, the compressive Young modulus of the single-crystal Cu increases, while the tensile Young modulus decreases, and that both the tensile and compressive yield stresses experience a dramatic decrease. To analyze the effects of vacancies and interstitials independently, the mechanical properties of the comparison samples, which only contain randomly distributed vacancies, are investigated. The results indicate that the vacancies are responsible for the change of Young modulus, while the interstitials determine the yield strain.