Fretting, which is a special type of wear, is defined as small amplitude relative motion along the contacting interface between two materials. The structural integrity of steam generators in nuclear power plants is very much dependent upon the fretting wear characteristics of Inconel 690 U-tubes. In this study, a finite element model that can simulate fretting wear on the secondary side of the steam generator was developed and used for a quantitative investigation of the fretting wear phenomenon. Finite element modeling of elastic contact wear problems was performed to demonstrate the feasibility of applying the finite element method to fretting wear problems. The elastic beam problem, with existing solutions, is treated as a numerical example. By introducing a control parameter s, which scaled up the wear constant and scaled down the cycle numbers, the algorithm was shown to greatly reduce the time required for the analysis. The work rate model was adopted in the wear model. In the three-dimensional finite element analysis, a quarterly symmetric model was used to simulate cross tubes contacting at right angles. The wear constant of Inconel 690 in the work rate model was taken as $K=26.7{ imes}10^{-15};Pa^{-1}$ from experimental data obtained using a fretting wear test rig with a piezoelectric actuator. The analyses revealed donut-shaped wear along the contacting boundary, which is a typical feature of fretting wear.