The high-profile trial is seen as a test of the military-installed government's tolerance of independent media, with activists fearing a return to autocracy three years after the Arab Spring uprising that toppled Hosni Mubarak.
The trial of the Qatar-based channel's journalists also comes against the backdrop of strained ties with Doha, which was a strong supporter of Morsi and his now-banned Brotherhood.
The 20 defendants, including well-known Australian reporter Peter Greste, are accused of supporting the Brotherhood and broadcasting false reports, after police shut down Al-Jazeera's Cairo offices following the military's July 3 overthrow of Morsi.
At today's hearing, six defendants, including Greste and Canadian-Egyptian Mohamed Fadel Fahmy, appeared in a caged dock wearing white prison uniform.
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Fahmy, who was Al-Jazeera's bureau chief and was arrested along with Greste in December, told the court his right shoulder "has been broken for 10 weeks and I sleep on the floor" in a cell.
"I ask you to free me on the guarantee from the Canadian embassy that I will not leave the country," he said.
Fahmy's father Fadel told AFP before the hearing that his son was innocent.
He added that prison authorities have not allowed him to get a needed operation.
Another defendant, Soheib Said, said he was "tortured by state security."
Without elaborating, he said he faced "physical and psychological torture" and had "asked to be checked (by a doctor) but nobody answered."
Before the hearing began, defendant Baher Mohamed shouted: "Journalists are not terrorists," as a bench full of security personnel separated those on trial from lawyers and reporters.