Kneeling on the Floor

Question: Why do some shuls give out paper before we bow to the floor on Rosh Hashana and Yom Kippur. Do we really need it?
Answer: There is a Torah prohibition to prostrate oneself on a stone floor (Vayikra 26:1). The Rishonim offer different reasons for this averah:

According to Rambam (Avodah Zarah 6:6), the Torah forbids this simply because that is how idolaters practice their Avodah Zarah. The Sefer Hachinuch (349) adds that while we don’t suspect one who’s bowing to have such intentions, nonetheless we are worried that others watching him do so may get the wrong impression.

The Kesef Mishna (in his pirush on that Rambam), however, explains that bowing on stone floor was restricted to the avoda in the Beis Hamikdash. As with other forms of avoda, it may not be performed elsewhere (See Megilla 22b).

Although mideoraisa it is only forbidden to prostrate with one’s hands and feet stretched out on a stone floor, the Rabbis extended this prohibition to include prostration without outstretched limbs and full prostration on a non-stone floor (Rema OC 131:8). While some are particular not to kneel at all, the Mishna Berura (131:40) writes that one may kneel even on a stone floor.

Thus Rambam (6:7) writes that the custom is to place a mat between one’s head and the floor while bowing in Shul. The Mishna Berura (621:14) writes that if necessary one can use one’s Tallis. While some Shuls give out paper to place under one’s knees, it seems that this was initially done to prevent one from dirtying one’s clothes.
In conclusion, if the floor is wooden or carpeted, there is no need to place anything down. Only if the shul floor is stone should one place something between one's head and the floor.

May we be zoche to prostrate ourselves properly along with the Kohen Gadol, speedily in our days.