Exodus 34 · a question people ask
Why did Moses cover his face?
Exodus doesn't give a reason. It gives the order of events. The people "were afraid to come near him" (34:30), yet Moses called them and they came, and he spoke with them (34:31-32). "When Moses was done speaking with them, he put a veil on his face" (34:33). He took it off when he went in before the LORD, and after he came out and spoke to the people, "The children of Israel saw Moses’ face, that the skin of Moses’ face shone; so Moses put the veil on his face again" (34:35). Exodus doesn't say whether the shining faded. Paul, writing to the Corinthians, calls the glory of Moses' face one "which was passing away" (2 Corinthians 3:7), and says Moses "put a veil on his face so that the children of Israel wouldn’t look steadfastly on the end of that which was passing away" (2 Corinthians 3:13).
The verses
“But if the service of death, written engraved on stones, came with glory, so that the children of Israel could not look steadfastly on the face of Moses for the glory of his face, which was passing away,”
“and not as Moses, who put a veil on his face so that the children of Israel wouldn’t look steadfastly on the end of that which was passing away.”