Call to Adventure: Miller is asked to lead a company of troops in an attack on Omaha Beach in 1944.
Refusal of the Call: Slight but noticeable when Miller steps off the ship with his comrades and seems to be frozen in time-- not giving any directions or orders.
Supernatural Aid: As men are getting their limbs blown off, and dodging constant fire, Miller, is able to help some men in this hell-like situation by giving orders or finding a safer spot for them to be.
Crossing the Threshold: Miller is then presented with the task of locating a man who had lost his brothers, and bringing him home to his mother. He fears the mission but knows that he has a duty to fulfill.
Tests, Allies and Enemies: Captain Miller faces danger, death of fellow soldiers, and emotional stress. Along the way, friendships form and enemies are killed, but not without a fight. During all this, Miller had to keep face and not let how he was feeling show in order to keep his men in better spirits.
Ordeal: The main ordeal is the actual journey to search for Private Ryan. There are "sacrificial victims", or soldiers, taken along the way. The journey took days and finding the will to continue was the hardest part.
Reward: Finally, finding Private Ryan.
The Road Back: Because of the Brotherhood that is formed during war, Private Ryan didn't want to leave his company. Miller and his men decided to stay with him until their job was over-- until they could get Ryan to leave with them, but unfortunately, Miller was killed before that could happen.
Return with Elixir: If Miller had survived the last battle, there is no doubt that he would have returned with elixir. Though he didn't live on physically, I know that his spirit and wisdom was instilled in his men.
ARCHETYPAL CHARACTERS
Hero: Captain Miller
Mentor: Miller doesn't have one. He is the leader.
Threshold Guardian: The entire troop that is assigned to look for Ryan isn't happy about it. Miller has to get these men, who he needs to want to go, to be positive about the mission.
Herald: General George C. Marshall presents the news to Miller in the form of a quote from an Abraham Lincoln speech.
Shapeshifter: Timothy Upham is initially assigned to accompany the troops as a translator because he can speak English, French and German. Before leaving, he reminded Miller that he hadn't shot a gun since Basic Training, but at the end of the film, he was able to dodge bullets and help the others reload ammunition.