You may transport unloaded firearms in a locked hard-sided container as checked baggage only. Declare the firearm and/or ammunition to the airline when checking your bag at the ticket counterI've written about this before, but it has been a long time. Rules may have changed by now, so the above link is effective as of this date.
If you are travelling by air, there are some strict regulations which you must follow considering how your firearms and ammunition must be stowed.
Firearms must be in locked, hard-side cases. The plastic case your gun came in does not meet standards.
Ammunition must be also in a locked, hardside case. Only shotgun ammunition may be stored in the same case as the gun. (As if that's going to be big enough!)
Ammunition must be in a solid container, not cardboard.
Note: if you're going to a match or on a hunt, it might be easier to ship the ammunition ahead to your destination as a separate effort. It's probably a lot cheaper, too, considering the cost of shipping it as 'luggage' considering the weight allowances.
I once flew to New York from Oregon to attend a match. When I checked the baggage, I discovered that the nice lady at the check-in counter was not aware of the regulations. I tried to demonstrate that my pistols (in checked baggage) were unloaded, and it freaked her out. She had no idea how to determine that the guns were unloaded, and when I took the locked hard-case out of the luggage and opened it up, she was frightened. She had never actually touched a gun before, so I racked the slide on each pistol to show that the gun was unloaded.
It was a great relief to her when I locked the case up and put it back in my locked hard-sided luggage.
The people in line behind me at the check-in counter breathed a sigh of relief, too, when the guns were locked back in the luggage and was whisked away by the attendant.
So, unless the counter person insists that you prove the gun is unloaded ... keep it low-key.
NEVER show a gun in an airport unless you are told to do so.
(It was an interesting experience .... one time.)
WARNING! DO NOT ALLOW ANYONE TO PUT A STICKER ON YOUR LUGGAGE THAT SAYS ANYTHING ABOUT A FIREARM INSIDE!
Baggage handlers were notorious about breaking into luggage with a sticker on it, and stealing your gun. Most airlines no longer require this kind of warning sticker, because they have been sued by too many people who have lost expensive firearms this way. NO reputable airline requires this; if the check-in clerk suggests that it is required, ask to talk to his/her supervisor. And check with the airline website before you confirm your reservation to determine if their regulations are out of date.
And print a copy of the regulations, along with the URL, so you can prove at the check-in counter what is and is not required.
Ammo presents a more complicated set of issues.
If you have several hundred rounds of ammunition in plastic boxes, that's legal.
But it's not secure, because the rough handling of the apes who load the ammunition into the plane can cause even the best-wrapped package to break into small pieces before it gets to the destination.
Again ... ALWAYS ship ammunition by FedEx or UPS to your final destination. Hotels will accept packages for pre-registered guests, and they don't need to know what's in them. However, you WILL need to prominently label the outside of the box to indicate the contents.
Shipping companies don't worry about boxes marked this way, and they are more gentle with the packages they receive.
Don't ship by parcel post. "Federal Employee", 'Nuff said. (Nothing personal, PostMan)
Oh, and if you're going to travel cross-continent to a match? Bring along extra 'small parts' and a good tool kit. Firing pin, extracter, ejecter, firing pin block, recoil spring plug (1911) ... you know best what parts will fail or be lost at a match far from home. I've had ALL of these parts (and others) fail or get lost during maintenance at matches. And when your extractor breaks or loses its tension during a match, ALWAYS have an extra which has already been tuned. Three rocks are all the tools needed to tune an extractor for a 1911, but it's an ugly process. (You know what are critical/vulnerable/easily lost parts for your gun, so consider this as just an example.)
... and a 1/8" punch will serve a lot of purposes.