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Recently the final worn shape of elastic indenters due to fretting wear was analytically solved using the method of dimensionality reduction. In this paper we extend this model to dual-motion fretting wear and take into account that the indenter is initially pressed with constant indentation depth and moved horizontally with constant displacement. Two key parameters, the maximal indentation depth during oscillation and the stick area radius in the final state as well as the liming shape of indenter are analytically calculated. It is shown that the oscillation amplitudes and the initially indented or moved displacements have an influence on the final shaking-down shape.