The whole concept of a rapture comes from an interpretation of a prophecy of Daniel's. Its in Daniel chapter 9 verses 24-27.
Note that a "septet" means "seven" (i.e. seven days - a week). The angel used the sevens concept deliberately for symbolic reasons rather than just giving numbers (e.g. seven "sevens" rather than just saying 49).
"Seventy septets are decreed on your people and on your holy city, to finish transgression, and to make an end of sins, and to make reconciliation for iniquity, and to bring in everlasting righteousness, and to seal up vision and prophecy, and to anoint the most holy. Know therefore and discern, that from the going forth of the commandment to restore and to build Jerusalem to the anointed one, the Prince, shall be seven septets, and sixty-two septets. It shall be built again, with street and moat, even in troubled times. And after the sixty-two septets shall the anointed one be cut off, and shall have nothing; and the people of the prince that shall come shall destroy the city and the sanctuary; and the end thereof shall be with a flood, and the war shall last until the end of the desolations that are determined. And he shall make a strong covenant with many for one septet: and in the midst of the septet he shall cause the sacrifice and the oblation to cease. From an extreme edge shall come an abomination, one that makes desolate, even to the full end of that determined, shall wrath be poured out on the desolate."
Seemingly endless interpretations of this prophecy exist. A serious problem is that historians can't definitely prove dates of when kings reigned. The same problem exists with Jewish history. Along with this there is question of just how we classify this command going forth to restore Jerusalem (as several commands went forth). This shouldn't have presented a problem to the people at the time, who would know the history first hand, rather than by interpretations of sometimes partially damaged tablets or conflicting written histories. Thus the interpretation of events referred to in this prophecy are subject to wide opinion now. It would be an enormous post all of its own to go through all the major opinions available.
Reading through the various opinions makes me think strongly on the advice in 2 Peter 1:20-21 about not making private interpretations of prophesies, but to use the Holy Ghost in such things instead. But I will share two of these interpretations. One that shows how the rapture concept has been connected with this prophecy, and one that opposes it. I'll begin with the latter as it is by far the more logical interpretation, because it doesn't make an unspecified interval, proposed by the former.
We have 69 (7 + 62) "sevens" prophesied before Christ(?) turns up. 69 X 7 = 483 days. It is presented that the Bible states that we should take a year for a day in prophecy (Ezek 4:6). Therefore we have 483 years. But it must be remembered that the Roman calendar didn't have a year 0. Thus we go from the year 1 BC to the year 1 AD.
It proposes that the beginning of the seventy septets occurred in 455 BC (the decree of Artaxerxes in his 20th year for Nehemiah). The 70th septet, therefore, begins in 29 AD when Christ began his ministry (according to the supporters of this interpretation). In 33 AD, 3.5 years (midway) into the 70th septet of years, the Messiah atoned for sins, thus causing the sacrifice and the oblation to cease, as prophesied.
However exponents of the rapture concept propose a different starting year and that the last septet of the 70 septets hasn't occurred yet. They refer to the statement, "And after the sixty-two septets shall the anointed one be cut off," proposing that this means EXACTLY at the end of the sixty-two septets (which come after the first 7 septets, thus equalling 69 septets) Christ would die, not during the 70th septet. This leaves us with a seven year period spare. They then propose that this 70th septet hasn't occurred yet.
They interpret events as such:
(the "sevens" are referred to as "weeks" in this translation)
A. Daniel 9:25 Jerusalem construction declared:
"Know therefore and discern, that from the going forth of the commandment to restore and to build Jerusalem"
B. Daniel 9:25 Prophecy of the Messiah:
unto the anointed one, the prince, shall be seven weeks, and threescore and two weeks:
C. Daniel 9:25 Jerusalem Construction happening:
it shall be built again, with street and moat, even in troublous times.
D. Daniel 9:26 Messiah dies:
And after the threescore and two weeks shall the anointed one be cut off, and shall have nothing:
E. Daniel 9:26 Jerusalem Destroyed by Romans 70 AD:
and the people of the prince that shall come shall destroy the city and the sanctuary; and the end thereof shall be with a flood, and even unto the end shall be war; desolations are determined.
F. Daniel 9:27 Messiah has pre-rapture of righteous as 7 years of devastation begins:
"And he shall make a firm covenant with many for one week: and in the midst of the week he shall cause the sacrifice and the oblation to cease" - they relate this to the prophesied evil beasts referred to in the Book of Revelation that will come before Christ's coming, saying that they will destroy the temple that will soon be rebuilt in Jerusalem.
G. Daniel 9:27 Jerusalem Destroyed again before Christ's second (third, according to the theory) coming:
"and upon the wing of abominations shall come one that makes desolate; and even unto the full end, and that determined, shall wrath be poured out upon the desolate."
However there are flaws in this latter interpretation. First, its whole basis for proposing a difference between the two mentions of Jerusalem being destroyed is that there are two mentions: Proposing they can't be the same destruction therefore: That we must read it as a continual story without repetition. Yet they are proposing a repetition of the things relative to the Messiah (Christ) and the sixty-two "sevens." Second, this text has Jerusalem destroyed completely the second time. Yet Zechariah tells us that an entire one-third of the population of Jerusalem will still be alive when Christ arrives for his coming (Zech 13:8). Third, it proposes an unstated interval of nearly 2,000 years - an amazing lot of supposition.
But what scripture texts stand as opposition to the idea?
"I don't pray that you should take them [his followers] out of the world, but that you would keep them for the evil one." John 17:15
This states that Christ isn't into removing his followers from the earth as an answer to coming problems.
"According to the Lord's own word, we tell you that we who are still alive, who are left till the coming of the Lord, will certainly not precede those who have fallen asleep." 1 Thess 4:15
So those who are alive won't be raptured before the dead. Note that he states "we". Therefore he wasn't anticipating any early rapture where they would be taken before the resurrection of those already "fallen asleep" (dead).
"For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever." 1 Thess 4:16-17
This not only states that the living won't precede the dead in being raptured, but that the dead will actually go first. Again note that he says "we". So this confirms that he didn't anticipated some early rapture.
"For the Son of man shall come in the glory of his Father with his angels; and then he shall reward every man according to his works." Matt 16:27
Here Christ is saying that it is at his coming that every man shall be rewarded, nothing about some being rewarded years before.
When giving the parable of the sower Christ says in regard the wicked and the righteous_
"Let both grow together until the harvest; and in the time of harvest I will say to the reapers, gather together the tares first, and bind them in bundles to burn them; but gather the wheat into my barn." Matt 13:30
This presents that Christ will destroy the wicked BEFORE gathering the righteous. It also presents that both should grow TOGETHER (i.e. not be separated until the final harvest).
Matthew chapter 24 contains signs of Christ's second coming. It talks of all the wars, pestilences and earthquakes we should anticipate. It talks of the "abomination that makes desolate" (or "abomination of desolation"). It talks of great tribulation.
Yet before it gets to the tribulation and abomination of desolation to come, it states,
"But he that shall endure to the end, the same shall be saved." (verse 13)
This suggests that the person is already a believer and needs to endure through the whole thing until the end - not to some pre-rapture.
While the idea of avoiding the worst of it sounds wonderful, the Scriptures don't support this concept. Not only isn't it supported, but they oppose it. It just comes out as another wishful thinking doctrine: A "wouldn't it be nice if."