Kim, I have used Strongboxes for many years. (I'm having trouble linking this, try this site:
https://secure.redmagnet.com/airfloatsys/strongbox.asp )They are sturdy and reusable heavy cardboard boxes with (optional) tough plastic liners. They're lined with two layers of "eggcarton" dark foam in which you can cut a shape to exactly fit your painting. Your painting rides nestled cozily to its destination. The whole thing is reusable and if you're mailing to an art show the repackers just pop it back in and the system comes right back to you if the painting is unsold. You can reuse the boxes many times. They are worth the investment if you plan to enter many shows. I would also use them to ship paintings to a client.
It seems to me that this company gives, or used to give, a discount to artists who are entering the Arts for the Parks national competition. It wouldn't hurt to ask.
I didn't fully appreciate these boxes until I helped uncrate paintings for a show last year. Show participants who shipped paintings haphazardly (one painting had seven layers of intricate tape and paper, a nightmare to unwrap) were thoroughly cursed by the unpackers.