The role of microstructure is quite significant in fretting because the scale of plastic strain localization near the surface is on the order of key microstructure features. A dual-phase Ti-6Al-4V alloy that tends to be susceptible to fretting is considered as a model material. Fretting is simulated using a two-dimensional finite element analysis. A crystal plasticity theory with a two-dimensional planar triple slip idealization is employed to represent the hexagonal close packed structure of the phase of Ti. Modifications of the slip system strengths enable multiple phases to be considered. In this study, the effects of grain orientation distribution, grain size and geometry, as well as the phase distribution and their arrangement, are considered in simulations. Implications of the results are discussed.