In mechanical power transmission systems, it is well known that the primary factor limiting the operational life of gears is severe tribological wear occurring on surfaces, rather than structural fractures. This wear process is a consequence of the elastic and plastic deformations induced by the high contact pressures generated between interacting tooth profiles. The present study focuses on the analytical calculation of these Hertzian contact stresses and the deformation characteristics triggered by such stresses. In the modeling based on the theory of elasticity, the contact geometry, and subsequently, the effects of the forces generated by the transmitted torque on the pressure distribution were numerically analyzed. Through the developed computational algorithm, the influences of design parameters such as pressure angle, radius of curvature, modulus of elasticity, and Poisson’s ratio on system performance were parametrically examined. The study specifically concentrates on minimizing contact stress and deformation parameters, which are of critical importance in external gear designs. To prevent stress exceedance, the fundamental cause of gear failure, nine distinct combinations comprising three different materials and three different torque options were investigated using advanced simulation techniques. Two-dimensional finite element (FEM) analyses, conducted within the Simulation environment of the Solidworks 2020 software, are presented in comparison with theoretical. It is observed that an increase in torque and the modulus of elasticity also leads to an increase in Hertzian pressure values  The consistency between the theoretical and numerical results demonstrates the accuracy of the analysis methodology and indicates that it can be utilized reliably in the design process. The fundamental reason steel emerges as an indispensable component in mechanical systems is the high volumetric strength efficiency it offers. In industrial gear manufacturing, a wide spectrum of materials is utilized, ranging from carbon-based alloys to alloy steels with complex metallurgical compositions. The primary parameters determining the material selection process are fatigue resistance under dynamic loading, ultimate strength, and the response of the material to heat treatment processes.