Gnashing (חרק) of teeth (שנים) appears several times in the Old Testament, including three mentions in Psalms, one in Job and one in Lamentations.
Lamentations says, of the Babylonian occupiers of Jerusalem, "שָֽׁרְקוּ֙ וַיַּֽחַרְקוּ־שֵׁ֔ן," "They hiss (שרק can also mean to weep) and gnash their teeth".
In all Old Testament instances, except Psalms 112:10, the gnashing appears to be an act of persecution and not suffering.
The phrase "(there shall be) weeping and gnashing of teeth" (in the Ancient Greek: ὁ κλαυθμὸς καὶ ὁ βρυγμὸς τῶν ὀδόντων) appears seven times in the New Testament as a description on the fate of the unrighteous ones at the conclusion of the age.
The phrase "gnash the teeth" is found in Acts 7:54, in the story of the stoning of Stephen.