Use the USPS supplied boxes. They are triangular shaped, very sturdy, and free from your local Post Office. They come in 2 lengths, 25" and 38". The 25" ones are great for shipping barrels.
PS I do recommend taping your barrel to a 1"X2" board and slipping it into the shipping box. It makes it very difficult for the shipper to bend your barrel without leaving significant evidence of mis-handling.