1 When Israel went out of Egypt, the house of Jacob from a people of strange language;
2 Judah was his sanctuary, and Israel his dominion.
3 The sea saw it, and fled: Jordan was driven back.
4 The mountains skipped like rams, and the little hills like lambs.
5 What ailed thee, O thou sea, that thou fleddest? thou Jordan, that thou wast driven back?
6 Ye mountains, that ye skipped like rams; and ye little hills, like lambs?
7 Tremble, thou earth, at the presence of the Lord, at the presence of the God of Jacob;
8 Which turned the rock into a standing water, the flint into a fountain of waters.
Princeton professor J. A. Alexander commented on Psa. 114:4:
The mountains skipped like rams, (the) hills like the young of sheep. As the Psalmist is reciting actual events, to be used as symbols and pledges of others, this cannot be explained as a poetical figure, but must be understood as referring to the concussion of Sinai, with its various peaks and neighbouring mountains. See Ex. xix. 18. Judg. v. 4. Ps. lxviii. 9 (8.) xcvii. 4, 5. Hab. iii. 6.
[The Psalms: Translated and Explained Volume III by J. A. Alexander. NY. 1852.]
The following are verses that mention earthquakes or mountains moving in the period of the exodus and occupation of the land.
And mount Sinai was altogether on a smoke, because the LORD descended upon it in fire: and the smoke thereof ascended as the smoke of a furnace, and the whole mount quaked greatly.
LORD, when thou wentest out of Seir, when thou marchedst out of the field of Edom, the earth trembled, and the heavens dropped, the clouds also dropped water.
O God, when thou wentest forth before thy people, when thou didst march through the wilderness; Selah:
The earth shook, the heavens also dropped at the presence of God: even Sinai itself was moved at the presence of God, the God of Israel.
He stood, and measured the earth: he beheld, and drove asunder the nations; and the everlasting mountains were scattered, the perpetual hills did bow: his ways are everlasting.
If Alexander was right, and the events were "actual events, to be used as symbols and pledges of others" then the question is, what are those "other" events that the expression "mountains skipped like rams" represent?
Paul tells us about the events of this period that "all these things happened unto them for examples: and they are written for our admonition, upon whom the ends of the world are come." [1 Corinthians 10:11]
This gives us a clue; if the mountains are the promises of God, and other revelations, (for example, Sinai represents the Mosaic law) then the ones that "skip like rams" must be the promises given to Abraham, that are applied to the Christians of all nations by Paul.
Mount Sinai, too, "skipped" from the desert to Jerusalem when Paul applied the label "Sinai" to Jerusalem in Galatians 4:25.
For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman.
But he who was of the bondwoman was born after the flesh; but he of the freewoman was by promise.
Which things are an allegory: for these are the two covenants; the one from the mount Sinai, which gendereth to bondage, which is Agar.
For this Agar is mount Sinai in Arabia, and answereth to Jerusalem which now is, and is in bondage with her children.
The name of the mountain took a mighty leap here. And Jerusalem, also, "leaped" into heaven when Paul said, "But Jerusalem which is above is free, which is the mother of us all." [Galatians 4:26]
The mountains which skipped like rams, and the little hills which skipped like lambs, were not literal mountains and hills. When those animals skip, they are completely airborne!
Evidently, the Psalmist extended reports about some limited natural tectonic shaking, such as could occur due to an earthquake, to a complete detachment of mountains from the earth, such as rams and lambs do, when they leap and skip. I suggest it is fulfilled by the "Jerusalem" of the saints becoming the heavenly Jerusalem rather than the earthly one, and by those who are in Christ becoming "Mount Zion," and "Israel," which includes all those who are "made nigh" to the promises by faith in Christ.