Officers are appealing for the public's help to trace Adam Mark, 37, who is serving a life sentence for abducting and raping a woman, as well as attempting to abduct and rape two other women and rape of a 12-year-old girl.
He was last seen outside the reception area at HMP Leyhill in South Gloucestershire at 7.30pm on Tuesday and is thought to have left some time between 7.30-9.30pm. He was still missing today.
Avon and Somerset Police said Mark is from West Yorkshire and has no connections with the police force area.
It is thought he may be travelling back to West Yorkshire.
He is described as white, about 5ft 6in tall, of medium build with short cropped brown hair.
He wears a diamond earring in his left ear, is clean shaven and has blue eyes.
He also has tattoos and when he went missing was wearing a grey tracksuit.
Police have advised anyone spotting him not to approach him but to call 999.
A Ministry of Justice spokeswoman said: "The level of absconding from open prisons in 2012/13 was the second lowest since records began.
"Absconds are still 13% lower than when this Government came to power. We are not complacent about this issue and are looking at ways in which the risk of absconding can be reduced further.
"We are committed to ensuring that risk to the public is minimised. All those located in open conditions have been rigorously risk assessed and categorised as being of low risk to the public.
Police said later that Mark was "exceptionally dangerous".
A spokesman said: "He was serving a life sentence after being convicted in 1996 of three rapes and one attempted rape of women and girls. He is considered to be a danger to the public and particularly children. On a number of occasions he has targeted women and girls alighting from buses or who were at bus stops as well as a woman walking her dog alone."
He added: "At this stage we believe he may still be in the Bristol area, and he has links to Yorkshire although it is possible he has travelled to other parts of the country."
Detective Inspector Jill Kells, who is co-ordinating the search for him, said: "Adam Mark is a very dangerous man. He is serving a life sentence for a series of stranger sex attacks against women and children as young as 12. He has also carried out robberies to fund his drug habit. We know he had started using drugs again before he absconded from prison.
"We are doing all we can to locate Adam Mark and return him to prison. We think he may still be in Bristol but we do not have confirmation of that so he could be anywhere in the country. If you see him please don't approach him but contact the police immediately by calling 999."
Anyone who knows where Mark has been since he absconded, or knows where he is now, was urged to contact police immediately on 101.