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According to the USPS web site:

What is required to mail a shotgun or other firearm to a family member?

Handguns may be mailed by a licensed manufacturer or dealer of firearms or an authorized agent of federal government.

Although unloaded rifles and shotguns not precluded are mailable, mailers must comply with the Gun Control Act of 1968, Public Law 90-618, 18 USC 921, et seq., and the rules and regulations promulgated thereunder, 26 CFR 178, as well as state and local laws.

For further advice on mailing a specific item, you should contact:

* The nearest office of the Bureau of Alcohol, Tobacco and Firearms (ATF)
* The Mailing Requirements area of your local Post Officeâ„¢ facility.