'Saving Private Ryan' is believed to have cost $70m to make; that would still be considered a fairly large budget now, but in 1998 it was huge. It therefore seems astonishing that $11m of that budget was spent on one scene, but that's what happened. You may even have guessed which scene it was already; that month-long shoot at Omaha Beach.
There were over 1000 extras involved in shooting the scene. That goes some way to explaining the cost, but then we have to factor in that these weren't just any extras. They were soldiers from the Irish Army Reserve, who had to be paid appropriately for their time. On top of that, around 30 of the extras were amputees, who were given purpose-built prosthetics to wear for their scenes, all in order for the prosthetics to be destroyed during battle scenes. The idea was to show the audiences graphic depictions of the kind of injuries real soldiers received in battle.