The painting should be in good condition even after rolling up it. If the painting is totally dry, then do not roll it up very tightly. Today most people take out the painting from canvas for transporting the canvas art. But you’ve to understand that when you roll it up many risks are involved in it. Folding up the art is not the perfect long-run option, so mostly avoid doing it.
To reduce the risk of damage, avoid rolling it up tightly always roll-up them as loosely as possible with paint on outer side. In case if you roll them with paint on inner side, the art could get crumple (particularly if they are applied thickly or if there is many textures).
If you are doubtful about this in your canvas art, you can test with quick test: fold your finger and find out what the skin does, on external edge they stretch out somewhat to match the curve, whereas on inner side they fold against inner part. Paint also does the similar thing.
Avoid rolling up the picture tightly; you should roll them as loose as possible. If you are going to put their picture into the tube for placing, then you should purchase the large-diameter one. Just purchase 2 tubes, the first tube is to roll up your canvas around hence they cannot get crushed unexpectedly, and another tube is to place their folded art into.
If you place anything over the picture before folding it then it will be problematic; you must protect the art however you do not need something that will stick with them, rub down on them, or scratch them. The art with certain textures like bubble wrap could get printed itself firmly on art (known as ferrotyping).