Michael Sicinski’s review published on Letterboxd :
The shift in venue and (above all) historical period means that it's unfair to expect the auteur / showrunner behind "The Thick of It," "Veep," and In The Loop to exactly reproduce his patented brand of breakneck repartee. But with The Death of Stalin, Iannucci stumbles a bit, partly because he is pulled in two incompatible directions. You can see at times that he wants to be funny, particularly as he casts caretaker General Sec. Malenkov (Jeffrey Tambor) in the role occupied by Tony Hale in "Veep" and Tom Hollander in In The Loop -- the self-important doofus who has climbed, as per the Peter Principle, to the level of his incompetence.
But so much of the subject at hand -- the mass executions and all-encompassing terror, in particular -- simply aren't funny. Comedy is not necessarily "tragedy plus time," and Iannucci recognizes this on some level. He is going for black humor with a genuinely mournful undercurrent, and one suspects the film is even supposed to "resonant with the present day," or something. But the U.S.S.R. depicted here is part Coen Brothers' glib cynicism, part Mack Sennett slapstick, with a dash of Downfall's hightoned verisimilitude, just to confuse matters.
The pacing is all off. If it's too rapid-fire, it risks seeming insensitive, but if it moves too slowly it becomes stodgy, so it just kind of lumbers along in between. Khrushchev (Steve Buscemi) struts and fidgets like a nervous carnival barker, while NKVD head Lavrenti Beria (Simon Russell Beale) lets his girth do the talking. Their jockeying for power too often takes the form of physical maneuvering, like who gets their car first out of the parking lot and in line for the funeral procession, or who makes it to Svetlana Stalin (Andrea Riseborough) to offer first condolences. It's as though Iannucci didn't understand how to depict political chicanery in a foreign (or real-life) context.
And when the final coup is set in motion, with the help of Red Army Field Marshal Zhukov (Jason Isaacs), Iannucci is a bit hamstrung. It involves the releasing of the trains into Moscow so that Soviet citizens may pay their respects to the late Stalin (Adrian McLoughlin), but it concludes with a massacre. So far, this has not happened on "Veep," so Iannucci doesn't exactly know how to depict it, or its aftermath, or how to enfold it back into the realm of black comedy. Instead it becomes a simulacrum of a mid-level period action film, clumsily staged and juiced with dramatic strings.
On the other hand, the execution of Beria feels less like a narrative comeuppance than a kind of pantomime. The failure of much of the film to convince, on either a comedic or a dramatic level, actually works here, because its artificiality demonstrates the show-trial aspect of upper-tier Soviet "justice." Beria's crimes are read aloud, and the assembled members of the coup pretend to be appalled. But the bullet is already in his head. They are all mouthing the words; history has spoken.