I don't know for certain, but I would think you could use plastic bins. You can when you're shipping with UPS or FedEx. You just need to make sure that the container fits within their size restrictions, and also that you tape it up really well.
If you do consider using a plastic container, be picky about the kind of plastic. Some are more brittle than others, and might not absorb shock as well. So, they'd be more prone to crack if, for example, they got dropped on one of their corners.