A heavily-pregnant teenager was found abandoned in Sheffield in what police described as a "shocking and tragic" case of people trafficking.
The victim told police that one of the men always wore sunglasses
The 16-year-old Kenyan girl was dumped on the city's streets after being held captive and forced into prostitution elsewhere, possibly in London.
Detectives have spent a fortnight building up a disturbing picture of what happened to the girl.
She had suffered "imprisonment, beatings and systematic rape".
Det Insp Matt Fenwick, of South Yorkshire Police, said: "Anyone who can subject a teenage girl to such abuse needs to be caught as a matter of urgency before they can do the same again."
Police have released an e-fit of one of the suspects. He wears sunglasses, and has two gold teeth.
Mr Fenwick said the girl remained "extremely distressed" by her ordeal.
"I'd ask anyone who thinks they may have encountered this girl or her captors to come forward - even if they were one of her clients."
Sheffield police began their investigation after the girl, who is due to give birth next month, sought help at council offices in the city centre last month.
The girl, whose mother died two years ago, had apparently been living on the streets of Nairobi until she was promised work as a house girl and brought to the UK at the end of last summer by boat.
She told police that violence and threats were then used to force her to work as a prostitute.
Police believe the house where she was held is in London.
Raids have taken place across the UK as part of Operation Pentameter
It is described as overlooking a park or grassed area and was split over three levels with some underground rooms and a white front door with glass in it.
Officers want to trace two men who drove the girl to Sheffield in a dark blue car on 16 June.
One was tall and black with a shaven head and always wore sunglasses. He spoke English and had two gold teeth - one upper tooth and one lower.
The other was white and spoke a language other than English. He had brown short hair.
News of the girl's ordeal comes just a month after it was announced that Sheffield would be the base for a new centre for combating human trafficking.
This follows the nationwide initiative Operation Pentameter, which identified 84 women who were believed to have been trafficked, 12 of whom were minors.