Police Scotland said Alice Byrne, 28, was last seen leaving a friend’s flat in Portobello a week ago.
The family of a woman who has been missing since New Year’s Day have said they are “shocked and distressed” by her disappearance.
Alice Byrne, 28, was last seen leaving a friend’s flat in Marlborough Street, Portobello, Edinburgh, between 08:00 and 10:00 last Saturday.
Detectives believe she potentially headed in the direction of the promenade and beach.
But extensive searches have failed to find any trace of Ms Byrne.
In a statement, released though Police Scotland, her family said: “Alice has been missing for one week now and we are shocked and distressed by her disappearance.
“She always keeps in contact with us so we are extremely worried because we have not heard from her. We are desperate to know where she is.
“If Alice sees this, we want her to know how much we miss her. We just want her home safe and well.”
The family urged anyone who has seen Ms Byrne or who has any information to come forward.
The statement concluded: “We are very grateful for the support we have received during this upsetting time.
“We would like to thank everyone who has shared appeals to find her, the police for their professionalism and especially the local community for all the support they’ve given.”
Chief Insp Kieran Dougal said no one has heard from Alice since she went missing.
He added: “As time passes we have become increasingly concerned for her wellbeing and safety.”
Searches of the Portobello area have involved specialist resources including air support, police dogs and the marine unit.
Chief Insp Dougal added: “We are aware that the beach and promenade area was busy on New Year’s morning so appeal to anyone to review photos and call if they have any information that may assist in tracing Alice.
“Naturally Alice’s friends and family are extremely concerned and we just want to trace her as soon as possible to ensure she is safe.
“Again, I would urge anyone who has seen Alice since Saturday, 1 January, or who has any information that may be relevant to our investigation to contact us as soon as possible. If Alice reads this appeal, please phone your family, friends or the police.”
Police have also urged anyone who was in the area at the time to check any dash cam devices.
Alice is described as white, about 5ft 6in, of medium build with short black hair.
She was last seen wearing a black top, black ripped jeans ripped and white trainers.