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Fretting fatigue problems occur in contact regions of two components submitted to contact loading and external cyclic loading or oscillation due to vibration. The contact region is submitted to micro-displacement relative with amplitudes in the rage 5 - 100 μm. The severe tri-axial stress state and local plastic strain can accelerate cyclic damage accumulation and premature crack nucleation. Under fretting conditions fatigue strength can be reduced by 50 to 70%, relative to conventional fatigue. The strength and life of components under these conditions is a difficult task, due to the complexity of the phenomena of contact and the various factors that control the process of damage accumulation. In this work, it was built a numerical model to study the fretting process in a sphere-plane contact for RQC-100 steel, using ABAQUS application. The model enabled the analysis of fretting cycles for different combinations of contact load and cyclic stress amplitudes.