Albert Barnes on Matthew 24:16

Then let them, etc. Then Christians may know that the end is come, and should seek a place of safety. Destruction would not only visit the city, but would extend to the surrounding part of Judea.

The mountains. The mountains of Palestine abound in caves, a safe retreat for those pursued. In all ages these caves were the favourite places of robbers; and were also resorted to by those in danger, 1Sam 13:6, 22:1, 2Sam 23:13, Josh 10:16. In those mountains they would be safe.