In this study that spur gears are chosen, contact stress of spur gear is presented under the effect of rotational speed. Three-dimensional simulation of dynamic analysis of gears designed and modeled using ANSYS software. The dynamic analysis included in the determination of dynamic stresses analysis. Contact stress is theoretically calculated and analyzed and numerically estimated using both Hertzian mathematical model and finite element method respectively. Different values of rotational speed used to study its effect on contact stress. Both methods compared by evaluating the percentage error of contact stress, and the modeling of the spur gear and stress analysis of spur gear carried out using SOLID WORK and ANSYS V14, respectively. The most significant note in this study concludes that increasing speed causes vibration and pitting failure due to repetitions.