The Browning Automatic Rifle M1918A2, commonly called the BAR, is a light machine gun that was developed by the Colt Patent Firearm Manufacturing Company for the United States Armed Forces during World War 2. The weapon was designed after it was clear that a machine gun was needed to dominate the trenches after World War 1. It was later developed by John Browning, just in time for World War 2. It comes in a variety of calibers ranging from the .30-06 Springfield and .303 British; to the 7.92x57mm Mauser and even the 6.5x55mm ammunition. It holds those types of ammunitions in 20 round magazines.
Saving Private Ryan
The BAR was seen in the hands of Reiben on D-Day and throughout the whole film while he was with Miller's Men when they were searching for Private James Ryan. It would appear to be his primary weapon, as supported by how Miller always wants him to use it.