Aidan McGuinness, 44, was reported missing from Hollesley Bay in Suffolk on Saturday morning.
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Joshua Lewis Terry, 29, and Levi Mitchell, 39, are then understood to have absconded together later that night.
Suffolk Police have launched a hunt for the three and have warned the public to stay away.
The force received a call that Terry and Mitchell were missing from the Category D jail at around 7pm.
Terry is serving a two-year and four-month sentence for affray, threatening a person with a blade or sharp-pointed article in a public place and theft.
He has been described as 6ft 2ins with ginger hair and blue eyes.
The lag has stubble facial hair and a tattoo on his lower arm of a star.
Mitchell is 5ft 10ins with ginger hair and blue eyes. He is of a slight build with a goatee beard.
The inmate, who is serving a sentence for multiple burglary offences, also has a birthmark on his left arm and hand.
McGuinness is 5ft 10ins with brown hair and blue eyes. He is of a thin build with a clean-shaven face and a slight northern accent.
Police said he has a tattoo on his left wrist that reads “Zara“.
He is serving a three-year sentence for theft, fraud and possession of Class B drugs.
Police have asked anyone with information to call them on 101 quoting CAD 310 or CAD 311 of 21 October.
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