3 to 11 casings can be found on the dead body of an enemy that was wielding a 10mm submachine gun or a 10mm pistol at the time of their death.
When you fire a weapon chambered in the 10mm round there is a 20% chance you'll get a casing, but that is reduced to only a 10% chance if you're using the JHP round.
You'll get 25 10mm casings if you buy a 10mm case box.
Occasionally some traveling merchants will "sell" 10mm casings (among many other calibers), but they will always be for free. Likewise, if you try and sell casings to a merchant, you will not yield any money.
