Depends.  Where I am, in hurricane country, shelter during an evacuation is not really an issue.  If you can't get a hotel room inland, then we would go to one of the many shelters that open up for such an event.  Biggest problem there is the bedding - I have foam pads and sleeping bags for the wife and kids - and food.
For the unlikely event I am caught without a man-made roof over my head, individually I also carry a poncho, poncho liner, a light wool blanket, some tent poles and stakes, and paracord.  I am thinking about getting a lightweight hammock to get me off the ground (I live in the almost tropics).
For the family, if we have to go I throw in the family tent. 
Hope this helps.
     .....CLIFF