Look at how cars are built ...

They're designed to crumple so that the force of an accident is "taken out" on the car rather than the people inside of the car. You can use something like Paper Mache (if you use thin layers with something light and spongy between them like cotton balls or packing peanuts it should crumple well) to build all or some of your container to take advantage of this concept ...

I did this in 10th grade and mine completely ruled. After it survived a 30 foot drop we tried a more extreme test. My teacher threw my egg container down as hard as he could from 30 feet and then before it landed someone else hit it with a metal bat and it still survived.

Here is how I made it:

The inner box is a plastic chinese container and the outer box is a soft cooler bag that looks like this

All of the squiggly circles represent balled up plastic bags. The plastic bags absorb a lot of force. 

^^^

well ,there you go.

I launched a container close to 100 ft without the egg breaking, actually. We made a rocked shaped design, put the egg at the base with minimal padding around 3 sides and a TON above the egg. Then, we weighted down the tip so that it would hit with the egg on top, and covered the whole thing in duct tape. I think we just got lucky with this, but it was still pretty cool.

You mean there are no restrictions other than what you can easily buy!? How lame is that?

Wrap your egg with these things in this order: bubble wrap, a small dish towel, cotton balls, and then place it all in a small lunch box.

This may be a bizarre idea, but what about a chicken. I've never seen an egg come out broken before so it must work.

Good luck putting it back in though.

@mistershine, hahahahaha. omg that is funny. You sir get +100.

damn, the chicken idea is gold. But take it a step further, and just drop trow and bend over when it gets to be your turn. If you survive the fall, the egg certainly will.

Just create as much drag on your container as possible. I did this when I was in the 3rd grade. I tied it to a plastic bag so it behaves as a parachute when I dropped it. I didn't think it worked too well. Try some balloons.

I saw this on a show called Mythbusters, put the egg in an 2 halves of an orange, followed by a balloon covering the orange any any other stuff you can find to make it even better....Also, a person called Jamie from Mythbusters did it really cleverly, ask me and I'll tell you what he did..