Usually you don't want to ship the PC in the box that the case came in. Why? Because they use low-grade foam which will break. Upon impact, the integrity of the case might be preserved, but drives can bottom out, and the foam oftentimes breaks so that a second impact will not be protected.
Try finding high-density dynamic foam to package your computers with, and then layer a thick shell of harder foam to create an exoskeleton. Then box it up and you *should* be good.
Something to consider is the case that you're using. Which model case did you build it in? Some cases simply ship better than others. As ugly as it is, the CoolerMaster Centurion 5 ships fantastically well, and the drives don't bottom out. Just make sure that you secure all of the drives, and do your best to organize the cables and secure them.
(I'm speaking from the position of working for a local computer company who ships dozens of PCs daily, just so you don't think I'm pulling this out of my butt 🙂