Can you ship a gun across state lines?

Provided you follow all the laws, yes.

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You may ship to yourself. If shipping to someone else, across a state line, it must pass through a Federal Firearms License (FFL) holder in THEIR state. This may be a dealer, collector, etc. You may ship a firearm to a gunsmith or manufacturer for repair (they hold FFLs) and they may return it to you. Long guns (rifles/ shotguns may be mailed by US Mail. Handguns must be shipped by a common carrier, such as UPS or FedEx. Exception- DEALERS may use US Mail for handguns, private citizens may not. Please note this does not apply to muzzle loading firearms- they are not considered firearms under Federal law, and can be mailed or shipped without a FFL.