Why will people hide in caves from the face of the Lord?
People will hide in caves and among the rocks because the great day of the Lord's wrath will have come, and they will be terrified to stand before the face of Him who sits on the throne and before the wrath of the Lamb.
When the Lord returns to set up His kingdom, Revelation 6 describes a scene of overwhelming terror on the earth. The heaven departs like a scroll rolled together, every mountain and island is moved out of its place, and the kings of the earth, the great men, the rich, the mighty, and every bondman and free man run to hide themselves in the dens and in the rocks of the mountains. They cry out to the mountains and rocks, begging them to fall on them and hide them from the face of Him that sits on the throne and from the wrath of the Lamb, because the great day of His wrath has come and no one can stand against it.
This fear comes because these are people who heard the truth but did not receive it. When they finally see Jesus coming in power, they understand exactly what is happening, and dread grips their hearts rather than joy. Revelation 1:7 confirms that every eye will see Him, even those who pierced Him, and all the families of the earth will wail because of Him. Zechariah 12:10 shows that even the house of David and the people of Jerusalem will look on Him whom they pierced and mourn bitterly, as one mourns for an only son.
Isaiah 24 adds that at this time the Lord makes the earth empty and turns it upside down, scattering its people without regard to their rank or station, because the earth has been defiled and its inhabitants have transgressed the laws and broken the everlasting covenant. So the impulse to hide in caves and among rocks flows directly from the unbearable dread of standing exposed before the wrath of God and the Lamb on that great and terrible day.
The scriptures
And the heaven departed as a scroll when it is rolled together; and every mountain and island were moved out of their places. And the kings of the earth, and the great men, and the rich men, and the chief captains, and the mighty men, and every bondman, and every free man, hid themselves in the dens and in the rocks of the mountains; And said to the mountains and rocks, Fall on us, and hide us from the face of him that sitteth on the throne, and from the wrath of the Lamb: For the great day of his wrath is come; and who shall be able to stand?
And I will pour upon the house of David, and upon the inhabitants of Jerusalem, the spirit of grace and of supplications: and they shall look upon me whom they have pierced, and they shall mourn for him, as one mourneth for his only son, and shall be in bitterness for him, as one that is in bitterness for his firstborn.
Behold, he cometh with clouds; and every eye shall see him, and they also which pierced him: and all kindreds of the earth shall wail because of him. Even so, Amen.
Behold, the LORD maketh the earth empty, and maketh it waste, and turneth it upside down, and scattereth abroad the inhabitants thereof. And it shall be, as with the people, so with the priest; as with the servant, so with his master; as with the maid, so with her mistress; as with the buyer, so with the seller; as with the lender, so with the borrower; as with the taker of usury, so with the giver of usury to him. The land shall be utterly emptied, and utterly spoiled: for the LORD hath spoken this word. The earth mourneth and fadeth away, the world languisheth and fadeth away, the haughty people of the earth do languish. The earth also is defiled under the inhabitants thereof; because they have transgressed the laws, changed the ordinance, broken the everlasting covenant. Therefore hath the curse devoured the earth, and they that dwell therein are desolate: therefore the inhabitants of the earth are burned, and few men left.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.