Do you have to have an actual cloth covering to rest your head on during tachanun? Or can you rest it directly on your bare arm (if you are wearing short sleeves)?
Furthermore, if you do indeed need a cloth covering, is it better to just not lay your head down at all if you are wearing short sleeves?
The Aruch Hashulchan (131:7) and Mishnah Berurah (131:3) both say that one should cover his face with a cloth and not merely one's hand, because a person's own flesh can't be considering a covering for itself.
If one is wearing short sleeves (assuming that one is allowed to pray in short sleeves...) than it appears that covering one's face with the arm alone is not prohibited, but useless (so it may be better to cover one's face with his arm anyway just to imitate everyone else). However, the Eliyah Rabba says that one shouldn't use the palm of one's hand. I think that in most cases though, even with short sleeves, you can stretch the sleeve to cover your face (I just tried it now, it seemed to work for me).
