Homer’s lavishly depicted Tantalus is the commonly known version but there is a second tradition attested in several of the major archaic poets that, while simpler, is not without its charm. First, the Odyssey (11.582):

καὶ μὴν Τάνταλον εἰσεῖδον κρατέρ᾽ ἄλγε᾽ ἔχοντα
ἑστεῶτ᾽ ἐν λίμνῃ: ἡ δὲ προσέπλαζε γενείῳ:
στεῦτο δὲ διψάων, πιέειν δ᾽ οὐκ εἶχεν ἑλέσθαι:
ὁσσάκι γὰρ κύψει᾽ ὁ γέρων πιέειν μενεαίνων,
τοσσάχ᾽ ὕδωρ ἀπολέσκετ᾽ ἀναβροχέν, ἀμφὶ δὲ ποσσὶ
γαῖα μέλαινα φάνεσκε, καταζήνασκε δὲ δαίμων.
δένδρεα δ᾽ ὑψιπέτηλα κατὰ κρῆθεν χέε καρπόν,
ὄγχναι καὶ ῥοιαὶ καὶ μηλέαι ἀγλαόκαρποι
συκέαι τε γλυκεραὶ καὶ ἐλαῖαι τηλεθόωσαι:
τῶν ὁπότ᾽ ἰθύσει᾽ ὁ γέρων ἐπὶ χερσὶ μάσασθαι,
τὰς δ᾽ ἄνεμος ῥίπτασκε ποτὶ νέφεα σκιόεντα.

Aye, and I saw Tantalus in violent torment, standing in a pool, and the water came nigh unto his chin. He seemed as one athirst, but could not take and drink; for as often as that old man stooped down, eager to drink, so often would the water be swallowed up and vanish away, and at his feet the black earth would appear, for some god made all dry. And trees, high and leafy, let stream their fruits above his head, pears, and pomegranates, and apple trees with their bright fruit, and sweet figs, and luxuriant olives. But as often as that old man would reach out toward these, to clutch them with his hands, the wind would toss them to the shadowy clouds.

For the alternative, Pindar’s Olympian 1.54-58 is the fullest surviving account:

εἰ δὲ δή τιν᾿ ἄνδρα θνατὸν Ὀλύμπου σκοποί
ἐτίμασαν, ἦν Τάνταλος οὗτος· ἀλ-λὰ γὰρ καταπέψαι
μέγαν ὄλβον οὐκ ἐδυνάσθη, κόρῳ δ᾿ ἕλεν
ἄταν ὑπέροπλον, ἅν τοι πατὴρ ὕπερ
κρέμασε καρτερὸν αὐτῷ λίθον,τὸν αἰεὶ μενοινῶν κεφαλᾶς βαλεῖν
εὐφροσύνας ἀλᾶται.

If in fact the wardens of Olympus honored any mortal
man, Tantalus was that one. He, however, could not digest
his great good fortune, and because of his greed he won
an overwhelming punishment in the form of a massive rock which the Father suspended above him;
in his constant eagerness to cast it away from his head
he is banished from joy.

A scholiast on these lines points to images in Alcaeus and Alcman. Alcman’s is curious for hinting at a blend of the two traditions – the rock as what blocks his pleasure rather than the spontaneous withdrawal of the goods. That reading of asmenoisin / agreeable things is very unclear, however.

καὶ Ἀλκαῖος δὲ καὶ Ἀλκμὰν λίθον φασὶν ἐπαιωρεῖσθαι τῷ Ταντάλῳ· <ὁ μὲν Ἀλκαῖος·>
κεῖται πὲρ κεφάλας μέγας, ὦ Αἰσιμίδα, λίθος.
ὁ δὲ Ἀλκμὰν οὕτως
†ἀνὴρ δ᾿ ἐν ἀσμένοισιν ἀλιτηρὸς ἧστ᾿ ἐπὶθάκας κατὰ πέτρας ὁρέων μὲν οὐδὲν δοκέων δέ†

Alcaeus and Alcman say that a stone hangs over Tantalus;

Alcaeus (fr 365):
“a great stone, Aesimidas, lies over your (my? his?) head”

and Alcman (fr 79)
“a sinner, he sat among agreeable things on a seat under a rock, seeing nothing, but supposing that he did.”

There’s also a fragment of Archilochus 91 referencing the same tradition (my pasting didn’t like the conjectural indicators under a few letters)

μηδ᾿ ὁ Τα]τάου θος τῆσδ᾿ ὑπὲρ νήσου κρεμάσθω

let the stone of Tantalus not hang over this island