An investigation by The Yorkshire Post found there were 24,653 reported cases in the 12 months up to June 30 – the equivalent of 67 every day.
The forces in West and South Yorkshire handled almost 19,000 of those cases between them, with one in every four involving a child in care.
And it is the apparent failure to stop children going missing repeatedly that is causing concern.
Assistant Chief Constable Mark Milsom, of West Yorkshire Police, said: “There can’t be a bigger crime issue that what’s going on here. Sitting behind it is the whole child sexual (CSE) exploitation issue.”
The link between CSE risk and children going missing repeatedly is well documented, but these children are also some of the most challenging to support.
One 16-year-old girl in care in Leeds, considered to be at risk from older men, is taking legal advice about her right to see who she wants.
Chief Superintendent Paul Money, Leeds Divisional Commander, said: “She’s still a child in the eyes of the law and certainly our focus is around safeguarding people like her and providing that general guardianship.”
The number of children in care going missing in Bradford has more than doubled, from 590 in 2014/15 to 1,303 in 2015/16.
And in neighbouring Leeds, there has been a 47 per cent rise.
Yet neither authority seems to recognise a potential problem.
Bradford Council said it had a “robust stance” in dealing with children reported missing. And Leeds City Council said it was effectively managing the issue strategically and on the ground.
But West Yorkshire Police Federation accused other agencies of passing their burden on by failing to stop people in their going missing in the first place. Chairman Nick Smart said: “It’s pushing the service to breaking point.”
This assessment of the pressure was shared by Mr Milsom.
He said: “Are the current care systems for vulnerable people, particularly vulnerable young people with CSE risk and people with mental health problems, under significant strain? Yes.
“Are the strains starting to show? Yes. Are the police going to be able to deal with it? We’re getting overwhelmed.”