A desktop computer tower holds a lot of weight in its power supply, graphics card, and drives, all mounted inside a metal case. Vibration on moving day can loosen those components, so the goal is to keep the case snug and cushioned. Combined with a solid backup, these steps protect both the machine and your files.
Pro tip: Reseat any cards and RAM at the new home if the machine will not boot. Vibration occasionally loosens connections.
Watch out: Heavy graphics cards can crack their slot under vibration. Brace or remove large cards for a long move.