If you do it by the book...here is a link. I think you hav to pay hazmat fees.
Shipping Ammo
This being said, I have bought ammo from a Hide member on several occasions and he shipped via USPS priority. He put ammo in a ziplock back 100 rounds per bag (5.56 and 7.62) and then wrapped each ziplock bag tightly with bubble wrap. He could get 300 rounds per medium box and put some more bubble wrap in there so everything was snug. Wrap each ziplock bag tightly so it doesn't rattle around.
I never had a problem. My postman never said a word.