Lynda Zefaj, 27, has not been seen since April 13, when she visited her parents in Glasgow.
Her mobile phone was discovered in Ayrshire, police have now revealed, adding it was found in a wheelie bin in Holmhead, Kilbirnie, on Thursday June 2.
Her silver Vauxhall Astra car was also spotted in Ayrshire on Wednesday April 20, on the A77 at Floak, with a damaged wing mirror.
Ms Zefaj, also known as Lynda Spence or Lynda Palmer, was last seen by her parents at around 6pm on April 13, when she left their flat in Partick. The next day her mother received a text from her daughter's phone saying she had gone to London.
Strathclyde Police Detective Superintendent Alan Buchanan said: "Despite our extensive searches and inquiries, we have yet to obtain any information on Lynda's whereabouts.
"As each day goes by, we are becoming increasingly concerned for Lynda's safety. Lynda has not been missing before and it is totally out of character for her not to contact her family.
"Understandably, Lynda's family are distraught and need to know she is safe and well. I would urge Lynda to contact her family or police as a matter of urgency.
"I would urge the person who found this phone to contact us. I would also appeal to anyone who was in the local area between 11am and 1pm last Thursday to come forward.
"The phone is a Nokia 2330 which is black and silver in colour."
Lynda is 5ft 8in, and has brown hair normally worn in a ponytail.
She has a scar under her eye.