Are the two witnesses Moses and Elijah?
Scripture does not name the two witnesses directly, but the powers given to them, shutting heaven so it will not rain and turning water to blood, closely match what Elijah and Moses did, so their ministry echoes those two great prophets even though they are not explicitly identified by name.
When you look at what the two witnesses of Revelation 11 are given power to do, the connection to Elijah and Moses becomes clear. Revelation 11:6 says these have power to shut heaven, that it rain not in the days of their prophecy, and have power over waters to turn them to blood, and to smite the earth with all plagues, as often as they will. This is placed right alongside the record of Elijah, who declared in 1 Kings 17:1 that there would be no dew or rain except by his word, and who later said in 1 Kings 18:15 that he would surely show himself before the Lord of hosts. Likewise, Moses turned the waters of the Nile to blood in Exodus 7:20 as one of the plagues brought against Pharaoh in Egypt.
The two witnesses are also called the two olive trees and the two candlesticks standing before the God of the earth in Revelation 11:4, language drawn from Zechariah 4, where two olive trees are described as the two anointed ones that stand by the Lord of the whole earth. This imagery of standing continually in God's presence is fitting for Elijah and Moses, since Elijah described himself as one who stood before the Lord, and Moses along with Elijah appeared together with Jesus at the Transfiguration in Matthew 17, both standing in glory in the presence of the Lord, talking with Him.
Beyond the shared powers and imagery, the two witnesses prophesy for 1,260 days, clothed in sackcloth, during the very three and a half years the Antichrist brings desolation upon Israel. They are eventually killed by the beast that rises from the bottomless pit, and their bodies lie in the street of Jerusalem for three and a half days while the world rejoices over them. After that time, the Spirit of life from God enters them, they stand up, and a voice from heaven calls them up, and they ascend into heaven in a cloud, followed by a great earthquake that kills seven thousand people.
So while the two witnesses are not explicitly named as Moses and Elijah, everything given to them, power over rain, power over water and blood, plagues, the picture of standing before the Lord as the two anointed ones, and their appearance together with Christ in glory, points strongly toward these two prophets as the pattern for their ministry.
The scriptures
And I will give power unto my two witnesses, and they shall prophesy a thousand two hundred and threescore days, clothed in sackcloth. These are the two olive trees, and the two candlesticks standing before the God of the earth. And if any man will hurt them, fire proceedeth out of their mouth, and devoureth their enemies: and if any man will hurt them, he must in this manner be killed. These have power to shut heaven, that it rain not in the days of their prophecy: and have power over waters to turn them to blood, and to smite the earth with all plagues, as often as they will. And when they shall have finished their testimony, the beast that ascendeth out of the bottomless pit shall make war against them, and shall overcome them, and kill them. And their dead bodies shall lie in the street of the great city, which spiritually is called Sodom and Egypt, where also our Lord was crucified. And they of the people and kindreds and tongues and nations shall see their dead bodies three days and an half, and shall not suffer their dead bodies to be put in graves. And they that dwell upon the earth shall rejoice over them, and make merry, and shall send gifts one to another; because these two prophets tormented them that dwelt on the earth. And after three days and an half the Spirit of life from God entered into them, and they stood upon their feet; and great fear fell upon them which saw them. And they heard a great voice from heaven saying unto them, Come up hither. And they ascended up to heaven in a cloud; and their enemies beheld them. And the same hour was there a great earthquake, and the tenth part of the city fell, and in the earthquake were slain of men seven thousand: and the remnant were affrighted, and gave glory to the God of heaven. The second woe is past; and, behold, the third woe cometh quickly.
And two olive trees by it, one upon the right side of the bowl, and the other upon the left side thereof.
Then answered I, and said unto him, What are these two olive trees upon the right side of the candlestick and upon the left side thereof? And I answered again, and said unto him, What be these two olive branches which through the two golden pipes empty the golden oil out of themselves? And he answered me and said, Knowest thou not what these be? And I said, No, my lord. Then said he, These are the two anointed ones, that stand by the LORD of the whole earth.
And Elijah the Tishbite, who was of the inhabitants of Gilead, said unto Ahab, As the LORD God of Israel liveth, before whom I stand, there shall not be dew nor rain these years, but according to my word.
And Elijah said, As the LORD of hosts liveth, before whom I stand, I will surely shew myself unto him to day.
And Moses and Aaron did so, as the LORD commanded; and he lifted up the rod, and smote the waters that were in the river, in the sight of Pharaoh, and in the sight of his servants; and all the waters that were in the river were turned to blood.
And after six days Jesus taketh Peter, James, and John his brother, and bringeth them up into an high mountain apart, And was transfigured before them: and his face did shine as the sun, and his raiment was white as the light. And, behold, there appeared unto them Moses and Elias talking with him. Then answered Peter, and said unto Jesus, Lord, it is good for us to be here: if thou wilt, let us make here three tabernacles; one for thee, and one for Moses, and one for Elias. While he yet spake, behold, a bright cloud overshadowed them: and behold a voice out of the cloud, which said, This is my beloved Son, in whom I am well pleased; hear ye him.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.