Jaime Cheesman disappeared when she was 16 years old, a few months after moving to Grimsby.
The former student, who would now be 39, grew up in Wellingborough, Northamptonshire.
Humberside Police said it is undertaking "an extensive forensic examination" of her last known address.
Officers are also searching the surrounding parts of Grimsby to piece together her last known movements, police said.
She was last seen in November 1993 in the Comber Place area of the town, where she lived with the family of her best friend.
Ms Cheeseman often travelled between there and her home town, according to her family.
During the week she went missing, she is thought to have left Wellingborough with her friend's father and another man to travel to Grimsby to sign on.
She may have become involved in a disagreement and left the house in Grimsby, police said.
Her disappearance is a "great source of anxiety" for her family, Det Ch Insp Phil Gadd, of Humberside Police, added.
"Her father has described Jaime as an outgoing girl with quite a few friends and feels certain that someone knows something about what happened to her.
"Whilst we believe there is a possibility that Jaime may still be in the Grimsby area, she was known to have connections with the travelling community in Northamptonshire and may have adopted this lifestyle in either area," he said.
Officers are searching a house where a teenager was last seen more than 20 years ago, just before she was reported missing.