Recently, various methods have been proposed to assess the risk of rolling contact fatigue failure and in particular, the Dang Van multiaxial fatigue criterion has been suggested in a simple approximate formulation by Ekberg, Kabo and Andersson. In a recent note by Ciavarella and Maitournam, it was found that the approximation is only valid in a restricted range of cases. Here, a much larger range of conditions including elliptical contact and partial slip conditions are considered and analytical formulae are also derived. The Ekberg, Kabo and Andersson calculation is shown to be a good approximation only for nearly circular contacts, high Poisson's ratio and high Dang Van constant. The Dang Van fatigue limits are very high, particularly for line contact: however, under those conditions ratcheting deformations also are likely to occur unless perhaps for very hard materials showing cyclic yield limit much higher than fatigue limit (these materials in turn could then show very low wear and be prone to fatigue crack propagation). Classical findings about the RCF fatigue suggest nearly twice higher fatigue limit in point contact with respect to line contact conditions, and this is apparently in contradiction to the Dang Van criterion. A possible qualitative explanation is that in point contact above elastic shakedown there is a regime of cyclic plasticity, rather than the direct transition to ratcheting regime as in line contact. However, the Dang Van criterion has been found to be possibly too conservative under RCF also by other authors recently, and further investigations are required.