According to the text of the Book of Mormon:
And when Alma had done this he departed out of the land of Zarahemla, as if to go into the land of Melek. And it came to pass that he was never heard of more; as to his death or burial we know not of.
Behold, this we know, that he was a righteous man; and the saying went abroad in the church that he was taken up by the Spirit, or buried by the hand of the Lord, even as Moses. But behold, the scriptures saith the Lord took Moses unto himself; and we suppose that he has also received Alma in the spirit, unto himself; therefore, for this cause we know nothing concerning his death and burial. (Alma 45:18-19)
It is interesting to note that our present Bible says that Moses "died there in the land of Moab, according to the word of the Lord. And he buried him in a valley in the land of Moab, over against Bethpeor: but no man knoweth of his sepulchre unto this day" (Deuteronomy 34:5-6). This is another instance which clearly demonstrates that Joseph Smith was not simply plagiarizing the Bible. Moreover, a purpose of the Book of Mormon is to establish the truth of the Bible.
Bruce R. McConkie says of the text in Deuteronomy: "the Old Testament account that Moses died and was buried by the hand of the Lord in an unknown grave is an error." . . . "It should be remembered that the Nephites had the Brass Plates, and that they were the "scriptures" which gave the account of Moses being taken by way of translation." . . . "Moses and Elijah were translated so that they could come with bodies of flesh and bones to confer keys upon Peter, James, and John on the mount of transfiguration, an event destined to occur prior to the beginning of the resurrection. (Matthew 17:1-6; Teachings, p. 158; Doctrines of Salvation, Vol. 2, pp. 107-111). The reason for the translation of Alma has not been revealed. [Bruce R. McConkie, Mormon Doctrine., pp. 805-806]
We might wonder if Alma's translation happened because of the desires of his heart to be an "angel" (Alma 29:1) and his desire to magnify his priesthood in the same manner as Enoch and Melchizedek (see Alma 12-13), who also had been translated (Joseph Smith Translation, Genesis 14:32-34). [See the commentary on Alma 29:1]
The reader should notice the symbolism of Alma's destination. Alma was going toward "the land of Melek," or in other words, "the land of the king" (in Hebrew melekh = king).
The reader should also note that in view of the concepts preached by Alma (the fulness of the priesthood of Enoch and Melchizedek), chapter 45 should have more fittingly ended after these verses describing the translation of Alma. [Alan C. Miner, Personal Notes]