A 21-year-old student who went missing in the early hours of Boxing Day left a note to her family "outlining her intentions", police said.
Sophie Smith, who was suffering from severe anxiety and depression, had previously talked about going into the sea to end her life.
She was wearing a vest and shorts when she left her home in Gorleston, near Great Yarmouth, Norfolk, at around 3am on December 26 last year.
Norfolk Police said it was "most likely" she had gone into the sea.
Inspector Will Drummond said: "We know from speaking to her family that Sophie had previously spoken about her intention to enter the sea to take her own life.
"Sadly, we can also confirm that Sophie had left a note and messages for loved ones, outlining her intentions."
Police have studied CCTV footage and said the last and only image of Sophie was at 3am on Boxing Day, running in the direction of the beach.
Sophie's mother Lynn Shaw said: "Sophie's step-father Kevin and I would like to thank the public and police for their continued support and dedication in searching for Sophie.
"In our hearts we hold every hope she will return safe and well.
"However, as a family, knowing the troubles she was experiencing, we do fear the worst for our little girl.
"Sophie had openly discussed how she was struggling and was receiving treatment.
"I would urge anyone suffering anxiety or depression not to fight that battle alone and seek help."
Sophie did not have her phone with her and has not accessed her bank or social media accounts since leaving home.
A Facebook page called Find Sophie Smith has gained more than 28,000 followers.