Intracytoplasmic sperm injection is an assisted reproductive technology in which a single spermatozoon is physically injected into the cytoplasm of an oocyte using a narrow glass needle. Over the past decade, rapid development of intracytoplasmic sperm injection (ICSI) has led to high demand on having precise injector motion and control during the injection task. Injector speed is a restricted dynamical factor in the injection task as it has a direct impact on the amplitude of the lateral displacement at the micropipette tip and therefore cell deformation creation. Analytical and numerical approaches have been instigated and the results have been compared to show the effect of injection speed on lateral displacement of the micro pipette tip. Euler-Bernoulli thin beam theory and the Matlab-Simscape Multibody dynamics simulation tool have been employed for analytical and numerical solution respectively. Cell deformation has been reported when evaluating the resultant lateral displacement of the micropipette during injection. It is found that this displacement helps to pierce the cell membrane during injection. This is due to additional stress created on the cell membrane. An optimal injection speed has thus been determined considering the lateral vibration induced by injection speed and cell deformation.