I would go a step further and submit that they didn't go to "heaven" but that our English language along with tradition has made the case.
Elijah is the easiest of the two to prove:
2Ki 2:11 Then it happened, as they continued on and talked, that suddenly a chariot of fire appeared with horses of fire, and separated the two of them; and Elijah went up by a whirlwind into heaven.
2Ki 2:12 And Elisha saw it, and he cried out, "My father, my father, the chariot of Israel and its horsemen!" So he saw him no more. And he took hold of his own clothes and tore them into two pieces.
2Ki 2:13 He also took up the mantle of Elijah that had fallen from him, and went back and stood by the bank of the Jordan.
So Elijah, via a whirlwind (tornado) went up into "heaven". But the word translated "heaven" is translated as the sky, the air, the cosmic realm (stars, planet, etc.) In context it is simply saying he went up into the sky...not the heavenly realm of God and the angels.
In other words, he was taken away by God so that Elisha could literally take up the mantle of prophet. Having Elijah there would have taken away from the authority of Elisha.
The proof?
2Ch 21:12 And a letter came to him from Elijah the prophet, saying, Thus says the LORD God of your father David: Because you have not walked in the ways of Jehoshaphat your father, or in the ways of Asa king of Judah, <
2Ch 21:13 but have walked in the way of the kings of Israel, and have made Judah and the inhabitants of Jerusalem to play the harlot like the harlotry of the house of Ahab, and also have killed your brothers, those of your father's household, who were better than yourself,
The letter from Elijah came AFTER he was taken up into the whirlwind.
So considering that there is NO way to be saved except through Christ this makes perfect sense...Elijah was taken away by God and moved to another place on earth so that God's work could continue with Elisha.
shâmayim shâmeh
shaw-mah'-yim, shaw-meh'
The second form being dual of an unused singular; from an unused root meaning to be lofty; the sky (as aloft; the dual perhaps alluding to the visible arch in which the clouds move, as well as to the higher ether where the celestial bodies revolve): - air, X astrologer, heaven (-s).
Guess it depends on whose Hebrew Lexicon you use, eh???