I'm not sure it is clearly stated. But some sort of rapture does make sense, as God doesn't judge His own people with the unbelievers (look at Lot, look at Noah, look at Exodus). I think the best passages giving evidence of it are below (also the imagery in Revelations), but I concede there is much that can be interpreted in different ways.
Matthew 24:36 - 43
36 But of that day and hour knoweth no man, no, not the angels of heaven, but my Father only.
37 But as the days of Noah were, so shall also the coming of the Son of man be.
38 For as in the days that were before the flood they were eating and drinking, marrying and giving in marriage, until the day that Noe entered into the ark,
39 And knew not until the flood came, and took them all away; so shall also the coming of the Son of man be.
40 Then shall two be in the field; the one shall be taken, and the other left.
41 Two women shall be grinding at the mill; the one shall be taken, and the other left.
42 Watch therefore: for ye know not what hour your Lord doth come.
43 But know this, that if the goodman of the house had known in what watch the thief would come, he would have watched, and would not have suffered his house to be broken up.
1 Thessalonians 4:14-17
14 For if we believe that Jesus died and rose again, even so them also which sleep in Jesus will God bring with him.
15 For this we say unto you by the word of the Lord, that we which are alive and remain unto the coming of the Lord shall not prevent them which are asleep.
16 For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first:
17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.