We consider fretting wear due to superimposed normal and tangential oscillations of two contacting bodies, one of which is an elastomer with a linear rheology. Similarly to the contact of elastic bodies, at small oscillation amplitudes, the wear occurs only in a circular slip zone at the border of the contact area and the wear profile tends to a limiting form, in which no further wear occurs. It is shown that under assumption of a constant coefficient of friction at the contact interface, the limiting form of the wear profile does depend neither on the particular wear criterion nor on the rheology of the elastomer and can be calculated analytically in a general form. The general calculation procedure and explicit analytic solutions for two initial forms, parabolic and conical, are presented for various combinations of frequencies and phases of normal and tangential oscillations as well as for various linear rheologies of the elastomer.