In this paper, electron impact ionization processes are incorporated in our Monte Carlo (MC) code for the calculation of the damage of the Bio-Molecules by the irradiation of X-Ray free electron lasers (XFELs). The study of this damage is useful for the analysis of three-dimensional structure of the Bio-Molecules using X-Ray free electron lasers because the damage appears as a noise for this analysis. The X-Ray absorption and Compton scattering processes take place after the X-Rays irradiate the target. Then, an electron is produced from atoms and moves in the target. This electron also gives rise to an electron impact ionization process for the other atoms or ions. It is assumed that electron impact ionization processes occur only when the electrons cross a cross section, which is located at the place of the atomic nucleus and is perpendicular to the direction of the electron velocity. The X-Ray flux, wavelength, and pulses of XFEL light pulses treated here are 10 20-21 /pulse/mm 2 , 0.1 nm, and 10 fs, respectively. We compare the frequencies of photo-electron impact ionization processes calculated by our MC code with those by rate equations. The relationship of these frequencies with shapes of targets using various ellipsoids as a target is discussed.