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I saw in the book, "The midrash says" by Rabbi Moshe Weissman that the Midrash Socher Tov 22 explains that a creature called R'aim lifted David into the sky (see here for details).

What is this animal R'aim?

Rav Slifkin, though not cited here as such, says it is most likely to be the aurochs.

It is treated fully in the aforelinked encyclopedia (volume 1), but he also addressed it incidentally in this essay.

From all the references in Scripture, we know the following about the re’em: It is similar to domestic cattle, but it is a powerful, dangerous animal, and it possesses two magnificent,
upwards-pointing horns. There is an animal that perfectly matches this description, and is even called rimu in Akkadian: the aurochs, Bos primigenius.

The aurochs (pronounced “oar-ox,” plural aurochses or aurochsen, and also known as the urus) was a huge wild ox that is familiar to few people today, because it became extinct
in 1627.

The reem (plural: r'aimim) has been described differently in various sources. Bottom line, it is most likely an aurochs.

Wikipedia has a good short summary

A re'em, [has been] variously translated as a unicorn or a wild ox. It
was first identified in modern times with the aurochs by Johann Ulrich
Duerst [...] This has been generally accepted, as it is today even
among religious scholars. It has been translated in some Christian
Bible translations as "oryx" (which was accepted as the referent in
Modern Hebrew) and as "unicorn" in the King James Version, possibly
referring to a one-horned rhinoceros such as Rhinoceros unicornis.

Writing on his Talmudology blog, Dr Jeremy Brown goes through various theories: wild ox, unicorn and rhinoceros. He then concludes it is an aurochs.

The most complete treatment comes from Dr. R Nathan Slifkin in his Torah Encyclopedia of the Animal Kingdom, vol. 1 pp. 278-286. He goes through various proposed translations and explains

• that it cannot be a rhinoceros since it didn't exist in biblical lands, has only one horn and is not kosher


• that it cannot be an oryx (reem in Modern Hebrew) as the reem is a dangerous animal while the oryx is shy and elusive - although after the autoch became extinct the name reem became transferred to the oryx


• that it cannot be a buffalo as they didn't live in biblical lands


• that it has to be the aurochs, a powerful and huge wild ox that became extinct in 1627. It matches the description in various verses of being huge, having massive horns pointed forwards and upwards, being aggressive and happening to live in the relevant area

See also Theresa Bane in her book Encyclopedia of Beasts and Monsters in Myth, Legend and Folklore.

See Gittin 68b where Shlomo Hamelech is talking to Athmedius King of Sheidim:

כתיב (במדבר כד, ח) כתועפות ראם לו ואמרינן כתועפות אלו מלאכי השרת ראם אלו השדים מאי רבותייכו מינן א"ל שקול שושילתא מינאי והב לי עיזקתך ואחוי לך רבותאי שקליה לשושילתא מיניה ויהיב ליה עיזקתיה בלעיה אותביה לחד גפיה ברקיעא ולחד גפיה בארעא פתקיה ארבע מאה פרסי על ההיא שעתא אמר שלמה (קהלת א, ג) מה יתרון לאדם בכל עמלו שיעמול תחת השמש (קהלת ב, י) וזה היה חלקי מכל עמלי

Shlomo Hamelech said to Athmedius: "The Passuk writes that "G-d has the power of the Toafos and the Reeim", Toafos are the ministering angels, Reeim are the Sheidim (loosely translated as demons). Shlomo asked:"I understand that angels are great. But Sheidim, why are they greater than us humans"
Athmedius resonded: "let me free from my chains and i will show you the greatness of the Reeim"

So Shlomo let him free from his chains and handed him his ring, Athmedius swallowed SHlomo Alive streched one wing out to heaven and one down to Earth (astronomical proportions) and spat him out 400 pharsangs (about 1600km) away and then Shlomo was ousted from his Throne and was left with just the clothes on his back and proclaimed: "What does one gain in all his labour under the sun? and this was my portion from all my hard work"

Sheidim have massive proportions as the Gemora mentions earlier 68a מטא דיקלא חף ביה שדייה מטא לביתא שדייה - that any palm tree or house that Athmedius brushed collapsed due to his large proportions so Sheidim could disguise themselves as a hill.(After all did Athmedius not disguise himself as Shlomo haMelech himself? See Gemora further)