Everybody has different methods for packing up models when moving, transporting them to contests, and so on. Here’s a way that I’ve been using to pack up my models for several years and I’ve never had any accidents or brokens pieces! 
It might be useful for other people or it might not.
I start by buying a plastic storage container that is longer, wider, and higher than the dimensions of the model.
After that, I then go to JOANNS craft store and buy some of their green foam. I prefer to look for leftover scraps that they have on their shelf as that might be cheaper. Their green foam regardless of size, shape, etc. is expensive. Try to buy it when it is on sale or use one of their coupons from their website if the foam is not on sale.
I usually buy a 1/2" or 1" inch thick foam “sheet” to lay on the bottom of the plastic tub.
After that, I lay my model on top of the foam and then plan out where I want to place smaller pieces/blocks of foam around the model to prevent the model from moving forward, sideways, etc.
I’ll use a hot glue gun to attach the smaller pieces of foam VERY CAREFULLY around the model. It helps to put the hot glue on the smaller pieces of foam first. Don’t put the hot glue on the larger bottom foam sheet while the model is still sitting on the sheet.
Another method might be to put your model on the bottom foam sheet, then take a marker and trace around the model on the foam sheet. Then remove your model. What you’ll have/see is an outline of your model on the foam sheet similar to the way crime scene investigators draw outlines with chalk around victims on the pavement. Then you can go ahead and hot glue small pieces of foam around that outline. When done, then you can place your model in the tub sitting on the foam.
If anybody wants to experiment with this packing method, I’d suggest trying it on some old scrap disused model kits first so you get a little bit of practice hot gluing foam around a model without accidentally getting hot glue “ON” the model. Be careful, folks. Hot glue is HOT! How do I know this? Trust me. I know. 
When I moved I used the stuffing that they use for pillows,I laid that in the box,put in the aircraft,then more stuffing so the plane wouldnt move.Plane was suspended between two layers of fluff.Didnt lose a missle or a pitot tube.
@WhatIfRebel, thanks for the packing tip. I’m filing this one away for future reference. My previous attempts at packing models did not go well.
You must have the luck of the gods. When I tried to use it the fluff snagged on every fiddly bit on the models and promptly ripped them off. No matter how careful I tried to be. What’s your magic trick?
I’ve got some bad news.
I just read on the news today that JOANNS is closing hundreds of stores across the country as they are filing bankruptcy for a 2nd time.
So for anybody who wanted to try my packing method using the green foam from JOANNS, I’d suggest you buy it before it’s gone. I’m not even sure what other places carry the green foam.
Otherwise, I think Hobby Lobby and Walmart carry packages of white cushion/upholstery foam that could be substituted if needed.