A gear is a critical component and can be found in many industrial applications. This investigation develops a three dimensional finite element spur gear model to calculate the contact stress on the gear tooth surfaces. Contact stress is one of the main factors that is used to decide the gears tooth surface strength. In addition there are other important factors such as frictional forces and micro-pits that influence the gear tooth surface. Different analytical techniques have been used to calculate the contact stress of the gear surfaces namely; Hertzian theory and AGMA standards. The analytical results have been compared to the numerical analysis to verify the spur gear finite element model.