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I have had good success with wrapping them in bubble wrap with the bubble side in. I use the small sized bubbles and wrap firm enough to stay on but loose enough to not break parts. Then they go in a zip lock bag labeled for what the model is.
When opening I open over a towel to catch anything that may have broken off. I often cut them open just to save handling.
When I moved my many-hundreds collection years ago, I utilized under-bed plastic boxes. These are just a bit taller than wrapped models, and were thus perfectly sized.
Each model was wrapped using bubble wrap. Roll the model in a section longer than the model, then fold and tape the ends to the top of the wrapped model.
I packed up my collection back in 2002 when I moved to GA. Each truck was wrapped in bubble wrap and then taped. They were then packed insde a good quality u-haul box. Some have not been out of the box since then due to moving every couple of years and no room to display them. The ones I did unpack were in good shape and showed no signs of problems.