Sophie Smith, who is from the Seacroft area of Leeds, was reported missing on Monday morning (16/5) and is thought to have voluntarily travelled with the man, who is not a relative, to the Bridlington area.
Investigations between Humberside and West Yorkshire Police have indicated that the pair have been seen in the Bridlington area on Tuesday afternoon where they are believed to have been looking for accommodation.
Sophie is described as around 5ft in height, slim build with a fair complexion, blue eyes and long black straight hair. She is thought to be wearing a black leather jacket, black leggings and grey boots.
The man Sophie is believed to be with is described as a white male, 5ft 10 inch tall, medium build with short, brown, cropped hair and brown eyes.
Officers are urging the pair to get in touch and are asking anyone who may have seen them around the Bridlington area to contact police.
Anyone with information is asked to call the Leeds Safeguarding Unit at Millgarth Police Station on: 0113 2414127 (office hours) or via: 0845 60 60 606 at any other time.