Police say they hold grave fears for the welfare of 35-year-old Rachel Funari, who was last seen on Bruny Island about 3.30pm on March 3.

Ms Funari is an American National who had been living in Victoria at the time.

She is described as being 165cm tall, of medium build with olive skin. She has a strong American accident.

Ms Funari was wearing a bottle-green full zip polar fleet jacket, black baggy lightweight pants, brown walking boots and prescription glasses.

At the time, she was carrying a Kodak disposable camera, a paperback novel, a small black clutch-style bag containing cards, papers and a single house key, as well as an older-style mobile phone in a multi-coloured sock cover.

According to police, Ms Funari arrived in Tasmania on March 1 and had been travelling with a medium-sized black backpack and a small tent bag.

To date, police have identified several places Ms Funari visited before she was reported missing:

- Tuesday, March 1: Ms Funari arrives in Hobart and stays at a resident in King Street, Sandy Bay, for two nights.

- Wednesday, March 2: Visits MONA at Berriedale and a coffee shop in Gregory Street, Sandy Bay.

- Thursday, March 3: Leaves Sandy Bay and takes the 9.30am ferry to Bruny Island.

- Thursday, March 3: Left alone at a shack at the end of Adventure Bay Road about 3.30pm. This is the last confirmed sighting of Ms Funari. Police believe that earlier that day she discussed walking the Fluted Cape Walking Track while on the island.

- Tuesday, March 8: Fails to board her return flight to Melbourne.

According to police, after finding her backpack, tent and belongings at the shack on Sunday, March 13, an extensive search operation was launched, focussing on the Fluted Cape area, as well as other tracks and popular tourist areas.

A five-day land, sea and air search, consisting of climbers, divers, police boats, the rescue helicopter and a specially trained cadaver dog failed to find any sign of Ms Funari.

Police ask that anyone who has any information to contact them on 131 444.