Anthony McCormick, 52, who was jailed for life for rape, and Nicholas Briggs, 28, walked out from HMP Leyhill in South Gloucestershire on Thursday.
McCormick is 5' 9" tall, and has links to Merseyside. Briggs is 6' tall and from the Newport area in south Wales.
Police say the men should not be approached and anyone seeing them should ring 999 immediately.
A convicted rapist and a man servicing a sentence for domestic assault have absconded from an open prison.