The movie is set in against the dusk of the Soviet Union and associated changes in economical and social life. Near one of Moscow's train stations, on a landfill site, a group of vagrants lives. Due to a variety of reasons, once prosperous people have lost their jobs, homes, loved ones and began living at a landfill. Among them are: Anthemia (Fima), a talented artist; her brother Fyodor Yelistratov, who was repressed in the days of Stalinism; Solomon, a former engineer, who lost his job because his family emigrated to Israel; and former cook and housemaid Katya, who was beaten and kicked out of her house by her drunkard son and got amnesia. The head of those unfortunate people is "President" - a former party worker Dmitry Loginov, who like his friend Fyodor, was in Stalin's camps.
One night the President tells his friends incredible news. He allegedly had contact with aliens, who promised to take all those people to their planet - to the place where happiness, joy and peace rule. At the right day and hour of the homeless are supposed to receive the signal from the "visitors from the sky": blue snow will fall.
They prepare for a long trip, but authorities are going to liquidate the landfill site to build a condom factory with American investors. The President and other inhabitants of the landfill are trying to protect their home, but the authorities in their pursuit to liquidate the camp of homeless people are ready to do anything.
At a winter night, "blue" snow begins to fall from the sky. The President and his "fellow citizens" go out to meet the good aliens, but they see heavily armed police squads and T-55 tanks approaching them that should raze vagrants' shacks to the ground.
Desperate people load on the old steam locomotive, power it up and as it gains speed, it takes off the ground, to the Promised Heavens.