Last year, I shipped stuff from Japan to the US in cardboard boxes and I had some successes and some problems. Maybe I can help you avoid the problems.
Joyful Honda sells cardboard boxes, in both double thickness and single thickness. Be sure to buy the double thickness. Joyful Honda also sells thin (3mm) sheets of plywood, and it turns out that the sizes are just exactly right so the plywood can fit inside the cardboard box and strengthen and stiffen the box tremendously without contributing very much weight. Since the boxes are made of rather soft cardboard, I strongly recommend doing this. The boxes I sent without the plywood lining suffered badly, but the ones with plywood lining survived perfectly. I only used 2 sheets of plywood in each one, so in principle the other two sides and the top and bottom were unprotected. Nevertheless, this was sufficient to make a nearly perfect and inexpensive shipping container. I think it is a good idea to make sure the plywood fits snugly.
By the way, I used the #22 size box which is also happens to meet (exactly) the airline restrictions on luggage/container size. I had no furniture or large items to ship, and I found the most economical method of shipping was to send heavy things (books) by mail, and pack everything else for the airplane. Even with the excess-baggage charge, it is still a reasonable way to send stuff, and it arrives when you do. I don't remember the exact cost now, but I think it was about 300 yen per kilogram. Of course there are limits on size, weight, and number of pieces. But you can send 4 excess pieces per ticket so if you're traveling with family, that's a lot of stuff.
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