But riot police set up barbed wire barricades to prevent them getting too close and plain-clothes officers filmed them.
The ambassadors of Great Britain, France, Germany and Italy were barred from entering the prison, but the US consul was reportedly allowed in, possibly to see Mr Yettaw.
Mr Yettaw was thought to be in the courtroom with Ms Suu Kyi on the first day of the trial, though it is unclear whether he was being tried as part of the case against Ms Suu Kyi.
There are no outside observers, but unnamed Burmese and opposition officials said proceedings had now been adjourned until Tuesday, after several hours of testimony.
A LIFE IN DETENTION
1988: Military junta comes to power after crushing pro-democracy uprising
1989: Martial law declared; opposition NLD leader Aung San Suu Kyi put under house arrest
1990: NLD wins elections; result rejected by the ruling junta
1995: Suu Kyi released from house arrest, but movements restricted
Sept 2000: Put under house arrest again when she tried to defy travel restrictions
May 2002: Released unconditionally
May 2003: Detained after clash between NLD and government forces
Sept 2003: Allowed home after operation, but under effective house arrest. In the years since, the orders for her detention periodically renewed
Mr Yettaw arrived on her back lawn in Rangoon earlier this month, after swimming across a lake using home-made flippers.
He was almost certainly uninvited, and Ms Suu Kyi's lawyers say she will plead not guilty to breaking the terms of her house arrest, saying he was allowed to stay only because he pleaded exhaustion.
Ms Suu Kyi's home is one of the most closely guarded locations in Rangoon, and her supporters believe the military authorities must have allowed the man to reach it, as he tried the same stunt unsuccessfully last November.
According to Burma's constitution, Ms Suu Kyi was scheduled to be freed on 27 May after six consecutive years of house arrest.
The misguided exploits of an apparently well-intentioned individual have now given the military government a pretext to keep her locked up, say correspondents.
Analysts say the trial shows that the military junta still fears Aung San Suu Kyi's influence over Burmese people, despite the fact she has been in detention for most of the past two decades.
They are keen to keep her detained in the run-up to the elections in 2010 - largely derided as a sham by the international community.
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