You'll see very few things on screen during 'Saving Private Ryan' that aren't correct for their time period or location. The guns, uniforms, locations and sounds are all as authentic as they could possibly be. Obviously, given the amount of time that's passed since the Second World War, many of the vehicles, planes and ships that were used at the time are long since obsolete, and have been scrapped. 'Many' doesn't mean 'all' though.
Spielberg found out that two landing craft of the type that were used in the Omaha Beach scenes were still intact, and in theory still sea-worthy. They were museum pieces, but Spielberg had them brought out of storage and tested. They were still capable of doing the job they were designed to do, and so they were used for filming. Even some of the vehicles seen on screen in this movie are war veterans!