Tariq Al-Daour, 21, from west London; Younes Tsouli, 23, from west London; and Waseem Mughal, 24; from Kent, are all standing trial at Woolwich crown court.
All three men deny charges under the 2000 Terrorism Act of possessing documents or records likely to be useful to a person committing or preparing an act of terrorism.
They are claimed to have posted extremist material on the internet, as well as distributing the videos, in an attempt to incite hatred of the western world.
The terrorist propaganda is said to have inspired suicide bombers across the world to carry out attacks against "non-believers".
On one of the videos alleged to have been distributed by the men, a background narrative is heard to say: "Here are the boys preparing for the attacks.
"They are showing us the stuff they are going to use for the attack.
"These boys are prepared to attack and Inshallah, God willing, they will attack Kuffar [non-believers] who are killing our brothers and Muslims in Iraq, in Afghanistan, Chechnya and many other countries."
The court heard how the men are alleged to have conversed with each other and contacts abroad in order to coordinate a programme for the distribution of the tapes and the posting of items on terrorist websites.
And evidence presented by Mark Ellison, prosecuting, said the men had been encouraged to "imagine how many [you have inspired] to become shahid [martyrs]".
The case continues.
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