Remember, the word "elect" has different meanings depending on the context. So in order to determine whether Israel or the Church is the "elect" in Matthew 24:29-31, let's consider the context of that passage. Recall that Jesus was a Jew living under the Old Testament Law of Moses, and He had not yet gone to the cross, and He had not yet been resurrected, and the Church did not yet exist, and there was no New Covenant or New Testament yet, and so on. Jesus was speaking to Jews (the disciples) who were still living under the Old Testament Law, and He mentioned the Jewish temple (Matthew 24:15), the Jewish prophet Daniel (Matthew 24:15), Daniel's "70 Weeks" prophecy concerning Israel's sins (Matthew 24:15), "those who are in Judea" (Matthew 24:16), the Jewish Sabbath (Matthew 24:20), and then He described the Second Coming and the "gathering" of the "elect." The entire context of these statements is Jewish in nature, and Jesus' audience of Old Testament Jews (the disciples) would have interpreted "the elect" as being the nation of Israel. They would not have interpreted "the elect" as being the Church because the Church did not yet exist, and there were not yet any "Christians," and there was not yet any New Testament teaching which described Christians as being "elect," and so on. The only "elect" group of people on earth at that time was the nation of Israel. In fact, even after the birth of the Church we still see the apostle Peter and "the apostles and the brothers throughout Judea" assuming that only the Jews were "the elect," because they were shocked when they first realized that "God has granted even the Gentiles repentance unto life" (Acts 10:44-11:18). So all of the evidence points to Israel as "the elect" in Matthew 24:29-31, not the Church. Now, when Jesus said that "he will send his angels with a loud trumpet call, and they will gather his elect from the four winds, from one end of the heavens to the other," what did this mean? To answer this question, notice that God had said that He would scatter people to "the four winds of heaven" and "the ends of the earth" and "the four quarters of the heavens" and "the four quarters of the earth," and He said that one day He will gather the Jews back to Israel with the sound of a great trumpet: "Therefore in your midst fathers will eat their children, and children will eat their fathers. I will inflict punishment on you and will scatter all your survivors to the winds. Therefore as surely as I live, declares the Sovereign LORD, because you have defiled my sanctuary with all your vile images and detestable practices, I myself will withdraw my favor; I will not look on you with pity or spare you. A third of your people will die of the plague or perish by famine inside you; a third will fall by the sword outside your walls; and a third I will scatter to the winds and pursue with drawn sword." (Ezekiel 5:10-12) "All his fleeing troops will fall by the sword, and the survivors will be scattered to the winds. Then you will know that I the LORD have spoken." (Ezekiel 17:21) ""Come! Come! Flee from the land of the north," declares the LORD, "for I have scattered you to the four winds of heaven," declares the LORD." (Zechariah 2:6) "I will bring against Elam the four winds from the four quarters of the heavens; I will scatter them to the four winds, and there will not be a nation where Elam's exiles do not go." (Jeremiah 49:36) "Do not be afraid, for I am with you; I will bring your children from the east and gather you from the west. I will say to the north, 'Give them up!' and to the south, 'Do not hold them back.' Bring my sons from afar and my daughters from the ends of the earth--everyone who is called by my name, whom I created for my glory, whom I formed and made."" (Isaiah 43:5-7) "The wolf will live with the lamb, the leopard will lie down with the goat, the calf and the lion and the yearling together; and a little child will lead them. The cow will feed with the bear, their young will lie down together, and the lion will eat straw like the ox. The infant will play near the hole of the cobra, and the young child put his hand into the viper's nest. They will neither harm nor destroy on all my holy mountain, for the earth will be full of the knowledge of the LORD as the waters cover the sea. In that day the Root of Jesse will stand as a banner for the peoples; the nations will rally to him, and his place of rest will be glorious. In that day the Lord will reach out his hand a second time to reclaim the remnant that is left of his people from Assyria, from Lower Egypt, from Upper Egypt, from Cush, from Elam, from Babylonia, from Hamath and from the islands of the sea. He will raise a banner for the nations and gather the exiles of Israel; he will assemble the scattered people of Judah from the four quarters of the earth." (Isaiah 11:1-12) "In that day the LORD will thresh from the flowing Euphrates to the Wadi of Egypt, and you, O Israelites, will be gathered up one by one. And in that day a great trumpet will sound. Those who were perishing in Assyria and those who were exiled in Egypt will come and worship the LORD on the holy mountain in Jerusalem." (Isaiah 27:12-13) Some of these passages describe the final regathering of the Jews back to Israel, accompanied by the sound of a great trumpet, and these passages are part of the Old Testament context for Jesus' statement that the angels will be involved in gathering "the elect," accompanied by the sound of a loud trumpet call. The nation of Israel will become saved immediately before the Second Coming, and then after the Second Coming all of the Jews will be gathered back to Israel. This is what Jesus was referring to in Matthew 24:29-31. The "gathering" of the Jews after the Second Coming in Matthew 24:29-31 does not refer to the Rapture, and in fact there will also be a separate gathering of the Gentiles (both saved and unsaved) after the Second Coming. Neither one of these "gatherings" is the Rapture, but instead they are gatherings of those who survived to the end of the seven-year Tribulation.