Poster tubes can be carried on airplanes as checked baggage and usually as carry-on luggage. Size restrictions must be met and if carried on, the tube must not have sharp edges or have other properties that could make it a weapon.
The TSA prohibits weapons and items that can be used as a weapon from being carried onboard a plane. While a cardboard poster tube is not prohibited, anything made of a heavy metal may not be allowed. Billy clubs and items that can be used in the same way are prohibited, and it is always up to the TSA agent to determine whether to allow you on the plane with a particular item.
A poster tube that's placed inside checked luggage needs to fit inside the suitcase, otherwise it will have to be considered a second piece of luggage or a special item. A poster tube carried onto the plane cannot be longer than the airline's stated maximum length for carry-on luggage.
Poster tubes that have sharp metal edges should be wrapped to protect TSA workers who go through checked baggage. Similarly, if a poster tube is made of a less sturdy material, bubble wrap it to ensure it does not get damaged.