Traveling on plane with models

When I take my stuff anywhere I make a box out of foam board/gator board for each kit and then line it with mattress foam that I can cut to fit the model.  That way I can keep the foam away from the fragile bits and support the kit in the strongest areas. Then put the individual boxes in your bag.  Keep in mind when packing that even if you're the only one carrying them they still may get turned upside down so it's best that they are supported from every angle.  Hope for the best but prepare for the worst.  

Carry-on rules and sizes have changed a lot lately.  Make sure the bag will fit or they WILL chuck it under the plane or worse, another plane.

I was going to say "bring some glue for repairs" but air security being what it is...

For figures, I use a tool box. I have a 1.5 inch styrofoam floor that can be cut for tall models. I use various sized foam walls held in place with toothpicks as well as the flexible foam that comes in many figure kits. This set up got me safely from Massachusetts to Arizona for an IPMS national by air and as far away as Rocheester by car. The toolbox is sized to fit the overhead. TSA folks were respectful in each direction. Large dios would be a real challenge for flying, however.

Yeah, no chance of getting them checked as baggage. I'll be carrying them on. I'm curious about how to best pack them so they don't slide, spill over, etc.

Don't let the baggage handlers, uhh, handle them. :(

I'm sure the vast majority are fine folks, but I've just seen wayyyyy to many leaked videos of carelessness and abuse. What's your carry-on situation?

Sounds like a good reason to move into 1:144 aircraft, 1:43 cars, 1:1200 ships :-)