In order to investigate the impact factors and their affection on high-speed precision multilink punch press (MPP), the dynamic model with different joint clearance was established, and the influence of different clearance and speed on the dynamic positional repeatability of bottom dead center (BDC) was analyzed. The elastic dynamic model of high-speed MPP was established, the affection of the elastic deformation and elastic wave on the positional repeatability of the BDC were presented by using modal superposition method to solve dynamic equation. Meanwhile, experiments on the dynamic repeatability of the BDC of the punch during working were completed. At last, the comparison of the experimental results with the analyzed results was given, and based on which, it can be concluded that the clearance, elastic wave and deformation are the key factors of the dynamic repeatability precision of the BDC.