On Friday, police reopened long-term missing person investigations of Eve Askew and Judah Zachariah Rueben Wolfe Mattathyahu.

Ms Askew was 14 when she disappeared on November 16 or 17 in 1991 from her family home on Gordon River Road in Fitzgerald, in the state's South.

She was living with her mum and dad and three siblings.

Police carried out extensive searches and interviews at the time.

She has not been seen or heard from since and a 2001 investigation failed to turn up any useful information.

Mr Mattathyahu was last seen alive 28 years ago, on or about November 11, 1983, at a property at Black Jack Road, Slopen Main, on the Tasman Peninsula.

He was about 49 at the time and was known to live a nomadic lifestyle, police said.

The Liberals have attacked Police Minister David O'Byrne for shutting the specialised unit six months ago as a part of budget cuts.

Opposition police spokeswoman Elise Archer said the unit's closure meant a lack of consistency would be a feature of future cold case investigations.

Mr O'Byrne said cold cases had been handed back to local criminal investigation branches, which received additional resources on a ``needs basis''.

``Tasmania Police is continuing to investigate cold cases, just as we said they would when the decision to disband the cold case unit was announced in July,'' he said.

Mr Mattathyahu may also have been known as Karl or Ruben Wolfe.

Police are asking anyone with information relating to his disappearance to call Crime Stoppers on 1800 333 000.

At the time of Ms Askew's disappearance she was 157 centimetres tall, of slim build, had red hair and was of fair complexion with freckles and was wearing a distinctive tracksuit.

There is a reward of up to $100,000 for information that results in a conviction in relation to the disappearance.

There is a direct line to investigators on 0418 589 544 for information in relation to the disappearance of Ms Askew.