One child aged six was missing for four days, while a teenager disappeared for 529 days, freedom of information requests have shown.
The NSPCC said the figures were "hugely concerning" as missing children are at risk of sexual exploitation.
Councils said they worked with agencies to protect and find them.
The data shows many of the children - who were mostly teenagers - went missing on multiple occasions.
Source: Freedom of information requests
Tom Rahilly, from the NSPCC, said: "Children go missing for many reasons - they're being bullied, they've been put in a home miles from their family and they miss them and their friends, or they just don't trust staff enough to tell them where they are.
"Many will have been abused before being placed in care and they need a lot of attention and protection."
In Torbay a 15-year-old disappeared on 11 separate occasions last year.
Torbay Council said it could not comment on individual cases but care plans were reviewed to ensure children and placements were matched correctly.
Plymouth City Council said: "In the case of a 16-year-old who was missing for 529 days, this refers to a young person from another country who did not want to remain in our care.
"We worked with police and other agencies to ensure that we followed all the necessary safeguarding procedures."
The council added it had a "thorough training programme" for foster carers and specialist support for those children affected.
Devon County Council said: "The number of children that have gone missing while in our care is very small, less than 3%, but any is too many."
It added that all children's social workers were undergoing new training to help them better support vulnerable young people.
Children went missing from council care in south-west England more than 350 times in the past five years, official figures have revealed.