A method for simulating fretting wear using the Modified Simplex Method for a contact solution has been developed. The initial separation between two contacting bodies was used as an input to solve the contact force distribution. An average cycle pressure distribution was calculated for the stationary surface over a displacement cycle. The wear depth was calculated for each body based on the modified Archard’s wear equation using the force distributions and the gross sliding distance. The initial separation was updated and the force distribution was solved for the next iteration. Methods for optimizing computational time are presented using a combination of linear jumping and adaptive cycle jumping for the wear depths, and an interpolation weighting method for reducing the grid size. It was found that computational time can be reduced by at least 98% compared with other simulation methods, making this method a viable tool for design. Fretting wear scars and depths were simulated for a cylinder on flat in contact and were found to agree with experimental results and Finite Element modeling results from previous literature. To show the capability of the fretting wear model, three practical applications were simulated: automotive seat sliding rails, steel wire ropes for industrial applications and steam generator tubes for nuclear power stations.