Gemara

18b (Mishnah): When they give to a Kohen Gadol the first meal after losing a relative, they sit on the ground, and he sits on a bench.

20a (Beraisa): An Avel (mourner) turns over all beds in the house.

(R. Yakov bar Ami): A bed with a beam attached above (on which a canopy is spread) cannot be turned over, therefore, a mourner just stands it up (on its head or back board).

Mo'ed Katan 15a (Bar Kapara - Beraisa): Hash-m says 'I put My image among you, and due to your sins, I reversed it (took it back). Turn over your beds (to show pain) over this.'

21a: Perhaps David was not obligated to stand when he tore his clothes, and he did more than he needed to.

Support: "He sat on the ground." (This was not obligatory.)

Question (Beraisa): If an Avel sat on a bed, chair, big mortar, or even on the ground, in all cases he was not Yotzei.

(R. Yochanan): He was not Yotzei inverting the bed.

Answer: He sat like on the ground (on an inverted bed).

27a (Beraisa): We erect beds (in an Avel's house) from the time of Minchah on Erev Shabbos.

(Rabah bar Huna): Even so, he does not sit on it until dark.

Rishonim

Rif (Mo'ed Katan 18a), Rambam (Hilchos Evel 13:3) and Rosh (3:98): The consolers may sit only on the ground - "va'Yeshvu Ito la'Aretz".

Nimukei Yosef (DH Ein): "Va'Yeshvu Ito" connotes that the consolers sit like the Avel does (on the ground).

Source (Gra YD 387:2): The Ramban and Tur (387) also cite this Drashah from the Gemara, and they cite another Drashah from this verse obligating the Avel to sit on the ground. This was in the Gemara; the printers omitted it.

Tosfos (21a DH d'Iy): How did the Gemara try to prove that David was extra stringent about sitting, and immediately ask that he did less than obligated?! Rather, the Gemara brought the verse to show that he (inverted the bed,) and also sat on the ground. You cannot say that he only sat on the ground, for if so he was not Yotzei. We conclude that perhaps he did not do anything extra.

Rambam (4:9): On the first day, the Avel must sit on an inverted bed. On the other days of Avelus, he may sit on a mat or on the ground.

Rebuttal (Ra'avad): I found no source (that he must sit on an inverted bed on the first day).

Ramach: I did not find any Ga'on or Meforshim who distinguish like the Rambam. Even on the first day, one who sits on the ground fulfills Avelus better! Mo'ed Katan 21a and the Yerushalmi say so.

Kesef Mishneh and Beis Yosef (YD 387 DH u'Mah she'Chosav b'Shem): R. Yochanan taught that he was not Yotzei inverting the bed (unless he sat on an inverted bed). I do not know the source to distinguish the first day from other days.

Migdal Oz: Zevachim 100b concludes that the first day of Avelus is mid'Oraisa.

Lechem Mishneh: Tosfos (and the Ra'avad and Ramach) hold like the Rosh, that if one inverted the bed he was Yotzei whether he sat on it or on the ground. The Rambam (and Beis Yosef) disagree. They explain that the Gemara suggested that the verse ("David stood and tore") is not precise and says an extra matter (that did not really occur). Similarly, it says "he sat on the ground", and surely this is not precise, for if so he was not Yotzei! We reject this; perhaps 'on the ground' means like on the ground, and the verse does not say anything extra.

Rosh (78): The Yerushalmi exempts one who lives in an inn from inverted bed, lest people say that he is a witch. People in Ashkenaz and France rely on this not to invert the bed, for they live among Nochrim, and they (Nochrim) are constantly in their houses. I saw in the name of the Ritzva that the heads of their beds did not stick out the way ours do, and it was evident that they were inverted. In our beds the head sticks out and it is not evident that they were inverted, so inverting does not apply.

Tosfos (21a DH Elu): Our beds have four poles sticking out on top (like legs), so one can sleep nicely also when it is inverted.

Rosh (ibid): If one inverted the bed and slept on the ground, he was Yotzei inverting the bed, and he did an additional matter. There is no Chiyuv to sleep on an inverted bed. Rather, inverting the bed is a Chiyuv, like Bar Kapara taught.

Tosfos (27a DH Min): It seems that our Gemara is the source not to sit on a chair or bench. It is not a solid proof. Perhaps a bed is different, for it must be inverted. We never find inverting a chair or bench.

Poskim

Shulchan Aruch (YD 387:1): An Avel the bed. When he sleeps and eats, he sits on an inverted bed. The entire day he does not sit even on an inverted bed, rather, on the ground. Also the consolers may sit only on the ground.

Beis Yosef (DH veha'Ra'avad): The Ra'avad, Ramban and Rosh say that he need not sit on an inverted bed. We follow them, especially because the Halachah follows the lenient opinion in Avelus.

Chidushei Hagahos (4): Even though the Beis Yosef brought a source for the Rambam, perhaps the Ra'avad's text discussed sleeping on an inverted bed (like the text of the Rif and Rosh). According to this, there is no source to sit on an inverted bed.

Rebuttal (Hagahos in Tur ha'Shalem 8): The Nimukei Yosef and the Beis Yosef himself say that the Ra'avad holds like the Ramban, that there is no source to sit or sleep on an inverted bed.

NOTE: To answer the question of Chidushei Hagahos, we can say that the Beis Yosef merely brought a source for the Rambam (according to the Rambam's understanding - see the Lechem Mishneh above), but he did not necessarily reject the Ra'avad's opinion.

Maharshal (brought in Taz 1): The Avel must sit on the ground only when consolers are there. Then, also the consolers must sit on the ground, unless the Avel pardons his honor and tell them to sit on chairs. Perhaps consolers do not sit on the ground nowadays because we assume that the Avel pardons his honor.

Taz (1): The Maharshal means that at other times the Avel may stand or walk. Surely, he may not sit on a bench!

Gra (1): Evel Rabsi (11) says that if one was sitting on a bed, bench or big mortar, and says that he will not invert the bed, we do not heed him. The Yerushalmi says that if he said 'I will not invert the bed. I will sit on a bench', we do not heed him, for he said that he will not invert the bed. If he agreed to invert the bed, we heed him (and let him sit on a bench)! It asked from the Mishnah, which allows only a Kohen Gadol to sit on a bench. It answers 'we distinguish between in public and in private. We do not do so', i.e. even in public we sit on a bench. In any case, we learn that one who inverted the bed may sit on a bench in private, and all the more so on the ground. The Shulchan Aruch requires investigation.

R. Akiva Eiger: One may sit on pillows and blankets on the ground.

Shulchan Aruch (2): Nowadays, the custom is not to inverted bed, lest Nochrim say that it is witchcraft. Also, our beds are unlike their beds, and it would not be recognized that they are inverted.

Gra (3): This is like the end of the previous Siman. (The Rema says that nowadays the custom is not to cover the head until the mouth; one should not be stringent about what out fathers did not do.)

R. Akiva Eiger: Even though the custom is not to invert the bed, it is proper to invert the pillows and blankets.