• First Secretary of the Communist Party of the Soviet Union – Nikita Khrushchev
• Chairman of the Presidium of the Supreme Soviet of the Soviet Union – Kliment Voroshilov
• Chairman of the Council of Ministers of the Soviet Union – Nikolai Bulganin

February edit

• 9 February – The report of the Pospelov Commission is presented to the presidium.
• 14–25 February – 20th Congress of the Communist Party of the Soviet Union
• 25 February – Nikita Khrushchev makes the speech On the Cult of Personality and Its Consequences at the 20th Congress of the CPSU.

March edit

• March – 1956 Georgian demonstrations

October edit

• 19 October – Soviet–Japanese Joint Declaration of 1956

November edit

• 4 November – United Nations Security Council Resolution 120 is passed.
• 7 November – The 2nd Soviet Antarctic Expedition leaves Kaliningrad
• 18 November – "We will bury you" is spoken by Nikita Khrushchev.
• 21 November – Soviet submarine M-200 is rammed and sunk by a Soviet destroyer, killing the submarine's crew.

• 13 January - Vladimir Merovshchikov, Russian professional football coach and former player
• 1 March - Dalia Grybauskaite, president of Lithuania^[1]
• 19 March – Yegor Gaidar, economist (d. 2009)^[2]
• 6 May – Vladimir Lisin, oligarch
• 10 May – Vladislav Nikolayevich Listyev, journalist
• 7 November – Mikhail Alperin, jazz pianist, member of the Moscow Art Trio, professor at the Norwegian Academy of Music (d. 2018).

• 3 January – Alexander Gretchaninov, composer

• 1956 in fine arts of the Soviet Union
• List of Soviet films of 1956