Lisa and Russell Squire, whose daughter Libby, 21, has been missing from her home in Hull since early on Friday, have made an emotional appeal for help in finding her, saying: "Please come forward with any information."
In the statement filmed by Humberside Police, Libby's father, Russell Squire, described his daughter as "our kind, thoughtful, beautiful girl, who is loved by so many people".
He appealed for people to come forward with any information "no matter how small or irrelevant it may be".
He added: "We just want you home."
Lisa Squire's voice broke with emotion as she spoke about her daughter.
She said: "Libby, my darling pie, we just want to know that you are safe.
"Please get in touch with us any way you can.
"The whole family is missing you, especially me and your dad, your sisters and your brother.
"I miss you so much it's breaking my heart not knowing where you are. I love you."
- Lauren Goodman, Libby's best friend
Libby's best friend Lauren Goodman also urged anyone with information to come forward.
Lauren said Libby would always let someone know she is safe, even if she were to lose her phone and not doing so is out of character.
Miss Squire was reported missing after getting into a taxi outside the Welly Club on Beverley Road, Hull, at around 11pm on Thursday, and is believed to have got out of the vehicle a short while later near her home address on Wellesley Avenue.
Humberside Police said she was then helped by a motorist who pulled over after spotting her on the street, with the force adding the man in question has since contacted them and has "really helped out" with the search.
Miss Squire was last spotted on CCTV on Beverley Road, near to the junction with Hayworth Street, at around 11.45pm on Thursday, the force added.
She is described as being 5ft 7in, with shoulder-length brown hair and was last seen wearing a black long-sleeved top, a leather jacket and a black denim skirt with lace.
A lipgloss and tools that were found near the search area are not connected to the investigation.
On Monday, officers continued to search the areas close to where Miss Squire was last seen.
On Wellesley Avenue, police dressed in black were searching in drains and wheelie bins along the street, while detectives conducted door-to-door inquiries in Haworth Street.
Nearby, officers from the police marine unit travelled along a length of the frozen Beverley and Barmston Drain in inflatable rafts, breaking the ice and searching the water.
Police also confirmed that officers were present in the University of Hull grounds to support the community.