The link immediately below may be referenced in it's entirety, but the pertinent data was cut and pasted into this post

Unprimed rifle, pistol or shotgun cases/hulls are fine.
Primed anything is NOT MAILABLE via USPS.

Pub. 52, Hazardous, Restricted, and Perishable Mail (Text)

341.2 Mailability, Packaging, and Marking Explosives are generally prohibited from mailing under 18 U.S.C. 1716. The following conditions apply to the mailing of explosives:
a. International Mail. All explosives are prohibited.
b. Domestic Mail via Air Transportation. All explosives are prohibited.
c. Domestic Mail via Surface Transportation. Generally, explosives are prohibited. The only exceptions are for Division 1.4S toy propellant devices and safety fuses that have been approved by the Manager, Business Mail Acceptance, USPS Headquarters, Washington, DC prior to mailing as stated in 341.22 and DMM C023.2.0.

c. Small Arms Ammunition. Ammunition is classified as a Division 1.1, 1.2, 1.3, or 1.4 explosive depending on the degree of hazard. Ammunition that is regulated as a Class 1 explosive and designed to be fired from a pistol, revolver, rifle, or shotgun, as well as associated primers and blank cartridges (including those designed for tools) and propellant powder for use in any firearm, is prohibited from mailing.

c. Shotgun Hulls, Empty Casings, Nonmetallic Shotgun Hulls, or Casings Without Primers. These articles are not classified as explosives or hazardous materials under 49 CFR, and therefore are mailable subject to the applicable mailing rules.