A new intrinsic methodology for the prediction of fretting fatigue failure of a structure is presented. It is based, first, on the evaluation of local relevant thermomechanical parameters by new thermoelastoplastic computational methods (direct cyclic method) and, second, on the systematic use of the Dang Van multiaxial high-cycle fatigue criterion. For the validation of this proposal, numerical simulations of fretting fatigue tests on a particular experimental setup considered as a structure are performed. The resulting prediction of the experimental fretting fatigue map in relation to plastic and fatigue material properties is good.