The criminals, one of whom has been locked up for threatening someone with a blade, all fled Hollesley Bay prison, near Woodbridge, on Saturday, as officers appeal for help in finding them.
Two of the men are believed to have escaped the Category D open prison in the evening together, while another left in the morning.
Suffolk Constabulary warned the public “should not approach them”.
The force received a report at around 7pm that Joshua Lewis Terry, 29, previously from the Norfolk area, and Levi Mitchell, 39, previously from the Hertfordshire area, had been reported missing.
It came after the force received a report at around 9.20am that Aidan McGuiness, 44, previously from the Barnsley area, had also been reported missing.
Terry is serving a two-year and four-month sentence for affray, threatening a person with a blade or sharply pointed article in a public place, and theft.
He is described as being 6ft 2 inches tall with ginger hair and blue eyes. He is of a thin build with stubble facial hair. He also has a tattoo on his lower arm of a star.
Mitchell is currently serving a sentence for multiple burglary offences.
He is described as being 5ft 10 inches tall with ginger hair and blue eyes. He is of a slight build with a goatee. He also has a birthmark on his left arm and hand.
McGuiness is serving a three-year sentence for theft, fraud, and possession of a controlled drug of Class B charges.
He is described as being 5ft 10 inches tall with brown hair and blue eyes. He is of a thin build with a clean-shaven face and a slight northern accent. He also has a ‘Zara’ tattoo on his left wrist.
Anyone who knows of the trio’s whereabouts or has seen any of them should contact Suffolk Police, quoting CAD 310 or CAD 311 or CAD 95 of 21 October.