For the benefit of those who are not as advanced in eschatology as some here, Ron, how about fleshing out why this relates to the rapture. I think it would be useful for those members and visitors because it is an interesting picture.
Sure. It helps to identify the players first. In the story in Daniel, the king Nebuchadnezzar represents the Antichrist. Daniel's friends, Shadrach, Mechach, Abednego represent believers during the Tribulation. Daniel is the church, the furnace represents the difficult time of the Tribulation. So, putting it together in a futuristic format.
During the Tribulation time, the AC will demand to be worshiped as God. The OT parallel is Nebuchadnezzar demanding the same.
Failure to do so will likely be death by various means. Again, the OT parallel is death in the furnace.
In the Tribulation, the Lord will protect his own, or many of them, many in the cleft city of Petra. In the OT story, an 'angel' appears alongside the men to
protect them, the 'angel' appearing as a 'son of the gods'. Probably Jesus in a theophany.
If the story is, in fact, a picture of the rapture/tribulation time, then the question is where is Daniel. He is, of course, not there. In the OT story, he is just
out of town on business. In the NT parallel, he is not there because, as the church, he is taken (raptured) before the difficulties begin. Thus, a pre-trib
rapture.
It's useful to note that, in a 'type' or 'shadow', all of the elements of the story do not have to line up exactly. For example, in the OT story, the three men are already believers, have been for some time. In the NT parallel, we know from other verses, that all of those who are in the tribulation will have been unbelievers, only becoming believers after the rapture. In this story, the three men are the only ones that we know of that were tossed in. In the tribulation, many believers will not be saved, the death count will be enormous. Nevertheless, the Lord will save many, some at Petra, some in other, undisclosed means.
In a similar vein, I see the rapture also in Noah and the flood, in much the same way. In that scenario, the flood is the tribulation time, the ark is God's protection of his own. Tribulation believers would be Noah and his family, God protecting them through the flood, not from the flood. So where's the church? Or maybe who's the church? Here, I think, it's Enoch, who was raptured some time before the flood began. Also, pre-trib. Hope this helps, RJS.
scriptures 
I Corinthians 15:52-57.
