Does the prohibition to fully prostrate oneself on a stone floor refer to one’s knees or one’s face (or both)? During Rosh Hashana and Yom Kippur, I see some people taking paper towels or cloth and putting them beneath their knees and others to prevent their faces from touching the floor.

We learn from the Gemara Megilla 22b, the Rambam (Hilchot Avoda Zara 6:7), Shulchan Aruch, Orach Chaim(131:8), that the main concern of Chazal in regard to "Even Maskit" (the prohibition of bowing on a stone floor outside the Bet Mikdash) is having one's face on a stone floor. Therefore, some poskim suggest that where there is nothing to place between oneself and the floor, one should turn his head to the side. Your question is truly in place at this time so people should not merely place small mats just to keep their knees clean. Gmar Chatima Tova and may we speedily return to the Bet Hamikdash.