Alice Byrne, 28, was last seen by her family at her home at around 2am on Saturday January 1.
She met friends in Marlborough Street and left a flat there between 8am and 10am on Saturday morning.
Police believe she may have headed towards the promenade area.
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It is believed the area would have been busy with the public and vehicles and it is requested that people in the area at the time check pictures, videos or dash cam footage that they may have for any sightings of Alice.
She is described as white, around 5ft 6ins in height and of medium build with short black hair. When she was last seen she was wearing a, black top, black jeans ripped at the knees and white trainers.
Chief Inspector Kieran Dougal from Craigmillar Police station said: “Alice is known to frequent the Portobello and New Hailes areas of Edinburgh.
"Since she was reported missing, officers have been carrying out extensive searches and enquiries in these areas. Local officers led by specialist search advisors have been assisted by resources including the air support unit, police dogs and our marine unit.
“Officers will continue to speak to people who know her and who live in the local community. Searches are continuing throughout the area and we would also ask local residents to check their outbuildings and sheds, as well as urging anyone with any information on Alice’s whereabouts to get in touch as soon as possible.”
“This is an upsetting time for Alice’s family who are extremely concerned that she has not been in contact with them since Saturday. This is completely out of character for her.
“I would again urge anyone who has seen Alice since Saturday morning, or anyone with information on her whereabouts to contact us as soon as possible. If Alice reads this appeal, I would urge us to phone her family, friends or the Police. Contact 101 quoting reference 0647 of 2 January.”