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This work investigates the characteristics of an involute elliptical gear system including, bending stresses, and the transmission errors of gears in mesh. Gearing is one of the most critical components in mechanical power transmission systems. Transmission error is considered to be one of the main contributors to noise and vibration in a gear set. Transmission error measurement has become popular as an area of research. To estimate transmission error in a gear system, the characteristics of involute spur gears were analyzed by using ANSYS. The contact stresses were examined using 2-D FEM models. The bending stresses in the tooth root were examined using a 3-D FEM model. Current methods of calculating gear contact stresses use Hertz's equations, which were originally derived for contact between two cylinders. To enable the investigation of contact problems with FEM, The results of contact stress from ANSYS are presented. These stresses were compared with the theoretical values from Lewis formula. Both results agree very well. This indicates that the FEM model is accurate.