I'm curious why one of the most prominent "social" sci. fi writers, Robert Sheckley, is almost unknown in the USA. Almost all his readers are outside of the USA. Why the guy's writings didn't touch many souls in his Motherland? Was he anti-American (in non McCarthy's sense)?

I recognize his name from having subscribed to the Magazine of Fantasy and Science Fiction for fifty years. But I can't say he rings a louder bell than that. Wondering why, I googled him and discovered that he is one of the few sci fi authors who writes with a sense of humor.

That's your reason right there. In America we tend to take our sci fi very seriously. Alan Dean Foster is the only American author I can think of who is celebrated in America and who also ventures into humorous territory. And he makes a good case study:

1. He writes both fantasy and SF, and most of his humorous work is in the fantasy genre, such as his Spellsinger series.
2. His humorous sci fi, such as "Quozl," doesn't get much respect. I've never met anyone else who read it.
3. He may be celebrated for his prosperity but not for his writing. He churns out several books per year so he makes a good living at it, but I never see him mentioned by "serious" critics, either mainstream or sci fi.

I must confess that I'm not terribly taken by humorous sci fi myself. "Quozl" is about the only book in that subgenre that I really liked. When I encounter stories of that type in F&SF, as often as not I quit reading after the first couple of pages. Most of it has to become a fantasy-SF hybrid in order to make itself work, and that is a really awkward hybridization. Wizards, neutron stars, spirits of the dead and FTL travel are very difficult to put together. Babylon Five did it in the medium of TV and pulled it off, but even there, humor was not one of its higher priorities.

Farscape had a lot of humor, without getting too deeply into woo-woo. I think it's easier to mix humor and sci fi in a visual medium rather than in print. And that may have as much to do with the difference in audiences as anything else. None of my sci-fi reader friends liked Farscape.

Sheckley is a kind of the "social" sci. fi writer in the sense that in all his works blasters, warp drives, gallactic fleet battles, semi-scientific mambo jambo, etc. are almost absent. He explored possible future social constructions and human behavior under those constraints. His humor is more like sarcasm of different extent of "obviosity" than humor per se. His death has become to some extent an illustration to his works.

What did he write? I've never heard of him.

Sounds a little like John Brunner. Except the funny part, of course.

Robert Sheckley (July 16, 1928 – December 9, 2005) was an American Jewish author. First published in the science fiction magazines of the 1950s, his numerous quick-witted stories and novels were famously unpredictable, absurdist and broadly comical. Sheckley was given the Author Emeritus honor by the Science Fiction and Fantasy Writers of America in 2001.

only Sheckley was an out-and-out satirist. During the 1950s Sheckley became the embodiment of the Galaxy Science Fiction writer and wrote stories of sharp satire using all manner of science fiction tropes and conceits.

[edit] Science fiction and fantasy novels
Immortality, Inc. (1958)
The Status Civilization, also known as Omega (1960)
Journey beyond Tomorrow (1963)
The 10th Victim (1966)
Mindswap (1966)
Dimension of Miracles (1968)
Options (1975)
The Alchemical Marriage of Alistair Crompton (1978)
Dramocles (1983)
Victim Prime (1987)
Hunter / Victim (1988)
On The Planet of Bottled Brains (with Harry Harrison, 1990)
Minotaur Maze (short, 1990)
Watchbird (short, 1990)
Bring Me the Head of Prince Charming (with Roger Zelazny, 1991)
Xolotl (short, 1991)
Alien Starswarm (short, 1991)
If at Faust You Don't Succeed (with Roger Zelazny, 1993)
A Farce to Be Reckoned With (with Roger Zelazny, 1995)
Star Trek: Deep Space Nine: The Laertian Gamble (1995)
Aliens: Alien Harvest (1995)
Godshome (1997)
Babylon 5: A Call to Arms (1999)
The Grand-Guignol of the Surrealists (2000)
Dimension of Miracles Revisited (2001)