A couple I remember hearing years ago from a Russian friend:
Comrade Lenin was out walking one day, and he came upon a young boy playing with some horse manure. “What are you doing, playing with horse manure?” Lenin asked.
“Comrade Lenin, I’m re-enacting the October Revolution,” answered the boy. “See, this piece of manure is the Aurora, firing the shots that set it off.”
Lenin nodded approvingly, and the boy continued. “And these pieces are the workers, rising up against the capitalists. And these pieces are the peasants, rising up against the landowners.”
Lenin was pleased, but he had a question. “Where am I? After all, I led the revolution.”
“Well, Comrade Lenin,” the boy replied, “I haven’t found the right piece of s— to represent you yet.”
Question: Why is the USSR able to buy wheat from Canada?
Answer: Due to a shortcoming of capitalism: overproduction.
Not really a joke, but it is cold war humor: A friend of my parents was a Russian language translator in Washington during the cold war. One night she and a bunch of co-workers went out drinking and got a little too drunk and started having a raucous discussion… in Russian… They refused to switch back to English until the police arrived and almost got arrested for being a bunch of Russki spies.
In the middle of a detente period, Gorbachev calls Reagan and says, “We have a little problem here; we’re almost out of condoms. Could you guys send us a few million?”
Reagan says, “Sure. We have a strong latex industry. A few million condoms shouldn’t be a problem.”
Gorbachev says, “Thanks, but since we’re Russians we need special condoms. They need to be 14 inches long and six inches wide.”
Reagan says, “Watch the mail.”
So then Reagan calls a buddy of his who’s a condom manufacturer and says, “Look. I’ve got a special order for you for delivery to Moscow. I need five million condoms 14 inches long and six inches wide. And I want you to print ‘Made in USA’ on one side and ‘Size: Medium’ on the other.”
Stalin loses his pipe. He looks and looks but he can’t find it. Finally he calls in Beria and reports the pipe stolen. Beria tells Stalin he’ll get right on the case.
An hour later Stalin discover’s he’s dropped his pipe into his boot. He calls Beria back and tells him he’s found the pipe.
“But comrade Stalin,” Beria says, “I’ve already had 10,000 people arrested!”
A family in Russia owns a parrot. They teach it to say all kinds of insulting things about Breshnev and to memorize every anti-Soviet joke there is. One day someone leaves the window open and the parrot flies away.
The family rushes down to the police station and tells the chief they’ve lost their parrot.
“What do you expect me to do? We don’t have him,” the chief says.
So the family tells him, “He’s bound to turn up sooner or later, and when he does, we just want you to know that we don’t share his opinions.”
In this newspaper, a CIA operative told a columnist that the agency planted a joke in Beijing, that went like this:
Mao sent a telegram to Moscow: CHINA STARVES. PLEASE SEND FOOD."
Khrushchev wired back: “TIGHTEN YOUR BELTS.”
Mao replied, PLEASE SEND BELTS."
But the Chinese were too clever for this. They planted the joke in Moscow; so instead of Mao, Khrushchev was out!