Fretting, a phenomenon caused by small oscillations between tightly fitted components under cyclic loading, leads to crack initiation due to high stresses at the contact interface. This process significantly affects the lifespan of various mechanical elements, including bolted and riveted joints, key-way shaft couplings, and blade-dovetail contact areas in turbine engines. This study investigates the contact stresses at the interface of two configurations—a cylinder on a flat surface and a ball-in-cup arrangement—using the Finite Element Analysis (FEA) package ANSYS and Hertzian Elliptical Contact Theory. The analysis considers mechanical cyclic loads and evaluates their impact on stress distribution. The study specifically examines steel components, commonly used in engineering applications, to determine the stress concentrations that contribute to fretting fatigue. The findings provide critical insights into contact stress behavior, aiding in the design of more durable mechanical connections.