http://www.lawyerintl.com/law-articles/ ... 20Aircraft
Edit: Forgot to cite the source.Finally, if you are flying in a private aircraft that is not being operated by a common carrier from one state to another, and no other statutes apply to your flight, you will still be subject to 18 USC §926A regarding the interstate transportation of firearms which states that "any person who is not otherwise prohibited by this chapter from transporting, shipping, or receiving a firearm shall be entitled to transport a firearm for any lawful purpose from any place where he may lawfully possess and carry such firearm to any other place where he may lawfully possess and carry such firearm if, during such transportation the firearm is unloaded, and neither the firearm nor any ammunition being transported is readily accessible or is directly accessible from the passenger compartment of such transporting vehicle".
This statute allows you to transport firearms between states subject to the statute's conditions: that you can lawfully possess the firearm at your points of departure and arrival, and the firearm is unloaded and inaccessible during the trip. However, what if you are a CCW permit holder and you want to carry concealed between states? Well, fortunately 18 USC §927 states that Section 926A does not pre-empt applicable state law. Thus, if you can lawfully carry a concealed weapon in the state in which you board the aircraft and in the state in which you land, you are not subject to the unloaded and inaccessible restrictions of Section 926A.
For operations of private aircraft within one state, you will only be subject to the laws of the state within which you are operating. You will need to review your state's statutes to determine whether they impose any restrictions on possession of firearms within non-sterile areas of airports. You will also need to be familiar with the airports you will be visiting to determine whether each airport has any restrictions (e.g. posting to prohibit concealed carry etc.).