The two accused, in their 20s, were produced in court on Monday in chains.
They pleaded guilty to the charge of insulting the monarchy in a play staged last year at Bangkok's elite Thammasat University. They face up to 15 years in jail under Thailand's Article 112.
That same day, Thailand's National Broadcasting and Telecommunications Commission (NBTC) summoned Internet service providers and said any website with content deemed in violation of Article 112 will be shut down by today.
Violations of Article 112 had spiked in recent months, NBTC's secretary-general Takorn Tantasith told journalists.
"We have to tighten the screws to prevent any further offences, or at least reduce them," he was reported as saying.
The move is part of what analysts say is an unprecedented crackdown on criticism of the monarchy by the royalist regime that seized power this year.
Analysts say this is meant to silence critics at a sensitive time, with a royal succession looming.
The widely revered 87-year- old King Bhumibol Adulyadej is frail. There is anxiety - expressed mostly in private for fear of violating Article 112 - over a future without his unifying moral authority.
The May 22 coup was launched by then army chief Prayut Chan-o-cha, ostensibly to avert what could have turned into a civil war as weeks of street protests, violence and political deadlock appeared to be coming to a head.
The army abolished the Constitution and wrote a new interim Charter.
Since the coup, 23 people have been charged under Article 112, says iLaw, an independent group monitoring legal cases. Of these, 19 are in custody, either awaiting or under trial.
Article 112 mandates that whoever defames, insults or threatens the "King, Queen, Heir Apparent or the Regent shall be punished with imprisonment of three to 15 years".
A feature of the law is that ordinary citizens can file complaints.
The accusation of disloyalty to the monarchy is a powerful tool in Thailand, often used to tar political enemies.
In an e-mail, Professor Thongchai Winichakul, who teaches South-east Asian history at the University of Wisconsin -Madison in the United States, wrote: "I don't think there has ever been abuse and enforcement of 112 like today.
"The number of cases, the scope (how the charge is applied to what actions) and the extent of unreasonable interpretations by the court - all are unprecedented."
A new committee chaired by Justice Minister General Paiboon Khumchaya will try to extradite Thais living abroad who have been charged with lese majeste.
However, analysts say the tactic is unlikely to succeed as it would be seen as being politically motivated.
Last week, Gen Prayut threatened to shut down media outlets that were overly critical of the government.
Martial law is still in force across the country.
Since 2006 - when the army first threw out a government led by then Prime Minister Thaksin Shinawatra - Thailand has been torn by a conflict that pits the conservative aristocratic elite and royalist middle class against what they see as a threat to the monarchy from corrupt and power-hungry politicians manipulating electoral democracy.
Political science professor Thitinan Pongsudhirak wrote in the Bangkok Post on Dec 26: "In this transitional period... a resurgent but outmoded political order must come to terms with new power arrangements."
Thailand's "virtual lockdown... is likely to be maintained", he added.
"We are on course to see greater militarisation and securitisation of Thai society and politics."
This article was first published on Dec 31, 2014. Get a copy of The Straits Times or go to straitstimes.com for more stories.