The 45-year-old from the Isle of Wight had been on a night out in Portsmouth city centre before going back to a flat in Southsea where she says the attack took place.
She was out on Saturday, September 27 with a friend before going back to the flat and reported the alleged rape to police on Sunday, September 28.
Three men have been arrested in connection with the rape allegation and police are conducting a thorough investigation.
Detective Constable Nick Bettesworth, the officer in charge of the case, said: 'It is believed the woman was an acquaintance of one of the men.
'We are still trying to find out what happened. The investigation is ongoing. A forensic investigation will commence alongside our investigation.'
Following the claim the woman visited the Treetops Centre (the Sexual Assault Referral Centre) with a Sexual Offence Trained Investigator (SOIT).
Det Con Bettesworth added: 'She is being supported by SOIT's and people at the Sexual Assault Referral Centre.
'Three men have been arrested but it is early days. We will hopefully be in a better position after our investigations.'
Officers from the Crystal Unit, (the specialist serious sexual assault investigation unit) questioned the men following the alleged incident.
Police say the woman is still in Portsmouth and has not yet returned to the isle of Wight.
Three men aged 24, 25 and 36 from Southsea were arrested and have been given police bail until November 19.
Anyone with further information should contact Det Con Nick Bettesworth at Fratton on 0845 045 45 45 or 01962 841534, or Crimestoppers anonymously on 0800 555 111.