The Swastika
The Swastika is one of the most recognizable symbols in all of history—and in Saving Private Ryan. It embodies the evilness of the Nazi party, which murdered millions of people simply because of who they were. In the end, the Nazi party is a powerful symbol of evil and blind hatred.
Weapons
Weapons that all of the characters use throughout the film, especially their M1 Garands, are symbols of the tools that soldiers use to wage war. Soldiers use weapons, particularly guns, to protect themself from enemy fire and enact their will on them.
France
France itself, the setting of most of the film, is symbolic of the way that areas are destroyed because of war. Because of their involvement in the war, France was reduced to tatters and their population was killed, maimed, and forced to leave.
Dead soldiers
Dead soldiers, which are littered throughout the film (but concentrated particularly heavily at the start of the movie), are symbolic of the sacrifices young men were often forced to make in the name of the greater good. The way that their bodies are treated by the enemy and their people underscores how little they are valued.
