Such re-enactments are standard police procedure in Thailand.
Earlier police said one of the men, named as Adem Karadag, was suspected of planting the bomb in the attack on August 17, contradicting what they had previously said.
The motive for the bombing, which killed 20 people, remains unclear.
Fourteen foreigners were among those killed.
Authorities now say they have enough evidence to prosecute the two men and say that Adem Karadag has confessed.
This contradicts earlier statements from police that neither of two men were the main suspects for the attack.
Adem Karadag, who has also been named as Bilal Mohammed, was arrested in late August in a raid on a flat on the eastern outskirts of Bangkok. His lawyer says he was not in Thailand at the time of the attack.
Police have released warrants for a total of 17 people over charges stemming from the attack.
The suspects are believed to carrying Chinese, Thai, Turkish and Pakistani passports, though their exact origins are unclear as some are thought to be using fake documents.
Many of the suspects named by Thai police have Muslim-sounding names, prompting speculation that they may be linked to jihadist networks or to Uighur separatist militants from China.
However, the police have not suggested that the attack was politically motivated.
The Erawan shrine – with its four-faced golden statue of the Hindu god Brahma – is considered sacred by Thai Buddhists, and attracts many foreign visitors.
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