A gun is untraceable if it cannot be traced to the person in possession of it or who committed a crime with it.

See Gun Traces.

There are basically two ways to acquire an untraceable gun.

The first way is to buy it through a private cash sale from someone who does not know you. If the gun is traced to the seller, and the seller cannot identify the buyer, then the trace has reached a dead end. This is legal in most states of the United States. However, it is uncommon. Few gun owners are willing to sell to a stranger with no questions asked, especially if it means the police might later accuse them of committing a crime with that gun.

The second way is to buy a stolen gun. Once a gun is stolen, it circulates on the black market. At most, a gun trace would reach the person from whom the gun was stolen, but they don’t know who stole it, so they can’t point investigators in the right direction.

Technically, a third way is to buy a gun that doesn’t have a serial number. Though serial numbers were common prior to 1968, manufacturers were not required to use them until the Gun Control Act of 1968, and unmarked guns are still in legal circulation.

A used gun is potentially untraceable, even if bought from a licensed dealer, because the previous owner(s) may be unable to direct investigators to that dealer. This isn’t a reliable method of acquiring an untraceable gun, but I mention this for the sake of creative writers, who may need to write about a failed gun trace.