The story of Buick Riviera is told through fates of two men, both Bosnian (ex Yugoslavian) emigrants, belonging to the two different religious groups that fought for the city of Sarajevo during the War.

Kingdom of Yugoslavia. As soon as she was born, Stana had both hands bit off by a pig, but she still grows to be good embroiderer. Her beloved brother Toma went into the city, where he's trying to make money by working in the circus. Toma comes to take Stana, promising her a better life in the city. However, she find herself left to the fate of circus act, and her brother eventually sells her to a...

Bobo, a young man, kills two criminals in self-defense. Afterwards, upon his lawyer's advice, he turns himself to the police. He ends up in a mental hospital from which he soon escapes and meets with his girlfriend. The police and a young ambitious reporter pursue him.