This paper presents qualitative elastoplastic simulations and analyses of fretting fatigue. Three hardening constitutive models are considered, and their effects on stick–slip conditions and lifetime prediction are compared. The computational analysis consists of the estimation of the shakedown limit cycle and the fatigue prediction using Dang Van or Crossland criterion. A particular configuration, the interaction of a flat pad with rounded corners in contact with a flat substrate made, respectively, of Inconel In718 and Titanium Ti64 alloys, is studied. The shakedown state is analysed using the cyclic and ratcheting equivalent strain concepts already discussed in the literature. In the paper, different fretting maps, based on slip, shakedown and fatigue regimes, are numerically produced and analysed. A new variable, the global slip percentage, is proposed for the characterization of the stick–slip regimes. Analyses of a series of slip maps show that the different hardening models do not introduce significant changes in the stick–slip conditions. Using finite element method simulations combined with fatigue limit criteria (Dang Van and Crossland), fretting fatigue maps are qualitatively reproduced. The main contribution of this work is a comparative discussion on the influence of the hardening models complexity on such maps.