Does Orthodoxy believe in the Rapture?

If you take away 7-year tribulations and barcode-666-computerphobia and the United Nations and the whole Israel subplot, the actual word rapture and the resurrection-and-meeting-Jesus-in-clouds part is definitely in scripture.

The Rapture is in 1 Ths 4:17: “We shall be caught up” in Latin is the verb rapiemur; the infinitive is rapere (to grab as a raptor grabs prey) and the noun form is rapture. (Biblical Greek uses the related verb arpázō with the same meaning: from this word come the harpies who flew down and snatched away the food from tables.)

Use in the New Testament:

• From the days of John the Baptist until now the kingdom of heaven suffers violence, and the violent take it by force (Mt 11:12).
• When any one hears the word of the kingdom, and understands it not, then comes the wicked one, and catches away that which was sown in his heart (Mt 13:9).
• See all 13 NT occurrences here.

What the Bible says about the Rapture

But someone will say, “How are the dead raised up? And with what body do they come?” … We shall not all sleep, but we shall all be changed in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised incorruptible, and we shall be changed… If we believe that Jesus died and rose again, even so God will bring with Him those who sleep in Jesus. For this we say to you by the word of the Lord, that we who are alive and remain until the coming [Parousia: presence] of the Lord will by no means precede those who are asleep. For the Lord Himself will descend from heaven with a shout, with the voice of an archangel, and with the trumpet of God. And the dead in Christ will rise first. Then we who are alive and remain shall be caught up [arpagēsómetha; rapiemur: we shall be snatched up] together with them in the clouds to meet the Lord in the air. And thus we shall always be with the Lord… And there will be signs in the sun, in the moon, and in the stars… for the powers of the heavens will be shaken. Then they will see the Son of Man coming in a cloud with power and great glory… Behold, He is coming with clouds, and every eye will see Him, even they who pierced Him… I was watching in the night visions, and behold, One like the Son of Man, coming with the clouds of heaven! He came to the Ancient of Days, and they brought Him near before Him. Then to Him was given dominion and glory and a kingdom, that all peoples, nations, and languages should serve Him. His dominion is an everlasting dominion, which shall not pass away, and His kingdom the one which shall not be destroyed (1 Cor 15:35–51; Lk 21:25-27; Rev 1:7; 1 Ths 4:14–17; Dan 7:13-14).

Hundreds of years before Dispensationalism was invented, this is what Anglican Charles Wesley refers to in his famous hymn: “Lo! he comes with clouds descending, once for favored sinners slain. Thousand thousand saints attending swell the triumph of his train. Alleluia! Alleluia! God appears on earth to reign.”