A "huge shortfall" of foster carers in England means 13% of children in public care will move between three or more homes in a year, a charity has warned.
BAAF says moving between carers can hinder children's development
Launching National Adoption Week, the British Association for Adoption and Fostering urged more people to adopt.
It said: "Many children in public care have suffered abuse or neglect and all are in desperate need of stability."
Some 4,000 of 78,900 children in public care in the UK are waiting for adoptive families, the association (BAAF) said.
It has launched a billboard campaign for National Adoption Week, which runs until 13 November.
Harm to children
The billboards read: "This poster has no permanent home. Like thousands of kids in care, this poster will be moved again tomorrow."
BAAF said: "As the billboards are moved from place to place, they will become increasingly damaged - mirroring the harm caused to children moved too many times."
BAAF chief executive Felicity Collier said many children meant to be adopted never were, because of a lack of adoptive parents.
The problem was particularly acute for groups of siblings, children who were older and those from black and minority ethnic backgrounds, Ms Collier said.
"Other children will move from one foster placement to another because of a huge shortfall in foster carers across the UK."
She said the charity was especially concerned about babies, with 12% of infants in public care in England being moved three or more times in the last year.
"There is evidence that a traumatic change like moving to live with a stranger you don't recognise can cause damage which may be irreversible to a baby's developing brain."
BAAF wants to see more schemes where foster carers are also approved as adopters, so children can stay with them permanently if it proves impossible to return to their birth families.
'Deprived of normalcy'
BBC radio and television presenter Nicky Campbell - who went into care when he was five days old - has lent his support to National Adoption Week.
"The day I was adopted by my mum and dad, Frank and Sheila Campbell, was the day I won the lottery," he said.
"You too can give the same chance to a child who is waiting for parents now and give them a loving home that they so deserve."
Samantha Block, 22, from Kent, experienced more than 20 moves and 10 schools during 13 years in care.
She said constantly moving deprived her of the chance to be a "normal child".
"It becomes harder and harder to make friends and in the end you don't see the point because you know you'll be moving on again soon," Ms Block said.
"My behaviour got worse and worse and then placements broke down more easily.
"I wish I'd had one family who could have helped me through my problems - it would have made all the difference."