Unless your tube is very light and flimsy, you shouldn't have a problem. (the tube wall thickness is the one to look at).
I have used tubes for posting all sizes of prints , from 10x12 inch to 20x30 inch and over all the years never had a problem with a crushed tube.
My method was to roll the print image side in, from the short side, roll the print around the outside of the tube, to avoid kinks..
Hold the rolled print and using my fingers slightly tighten the roll at either end, put a sheet of paper around the middle of the rolled print and tape it and insert it into the tube. Then tape the tube end stoppers.
Always use a tube slightly bigger than the smallest side of the print. EG: for 20x30inch print use a tube 22inches long.