The film opens just as construction has been completed on a railway connecting a mountainous regions of eastern Bosnia and western Serbia in 1992. Luka, a Serbian engineer, has moved to Bosnia from Belgrade with his mentally unstable wife, Jadranka, and his football-playing son, Miloš, to run a railway station and act as caretaker. Luka is at work preparing the opening of the railway while Miloš attempts to become a professional footballer with the Partizan team. Utterly engrossed in his work and blinded by natural optimism, Luka remains deaf to the increasingly persistent rumblings of war, which has broken out in Croatia and threatens to spread.
When the conflict explodes, Miloš is denied his place on the football field when he must join the Serbian army, and Jadranka disappears on the arm of a Hungarian musician. Eventually, he receives news that Miloš has been taken prisoner of war. Luka considers suicide, but a profiteering acquaintance presents him with Sabaha, a Bosnian Muslim whom he has taken hostage.
Luka intends to exchange Sabaha for Miloš, but the two fall in love after they are forced to flee deeper into Serb-controlled territory. When a UN-enforced prisoner exchange is finally arranged, Luka and Sabaha try to escape to Serbia, but Sabaha is wounded by a Bosnian sniper as they attempt to cross the Drina river. Army nurses narrowly manage to save Sabaha's life, and she is exchanged for Miloš, along with other prisoners. Jadranka also returns, and the family is reunited in their old home, but Luka is lovesick. He lies down in front of a train, but when the train stops to avoid running over a mule, it is revealed that Sabaha is on board, and the two ride away on the mule.