Mark Price, 39, and Reece Baker, 23, both absconded from HMP Kirkham at around 9.40pm on Monday (March 23).
Price had been sentenced to seven years and nine months in prison for offences including attempted robbery, breach of a restraining order, dangerous driving and assault at Birmingham Crown Court in January 2018.
Baker was jailed for seven years and seven months for robbery at Bristol Crown Court in December 2017.
Police are now appealing to the public for information about their whereabouts.
A spokesperson for Lancashire Police said: "Police are appealing for information and urging anyone who has seen either men to come forward".
Price is described as white, 5ft 10in tall, of slim build with dark hair and brown eyes.
He may be clean shaven, according to police.
Price has a tattoo of a jack in the box on his right arm.
He has links to the West Midlands and West Mercia areas.
Baker is described as 6ft tall, of slim build with brown hair and blue eyes.
He speaks with a West Country accent and has tattoos on his right arm including a rose and angel.
Baker has links to Avon and Somerset.
Anyone who has any information about their whereabouts should contact police by calling 101 or emailing [email protected]
In an emergency call 999.