More than 4,600 'assessment of need' applications for children with disabilities are overdue completion.
Over 3,250 are at least three months overdue.
An 'assessment of need' allows children to be diagnosed with a disability, such as autism, and then apply for the care they need.
The HSE is supposed to have these assessments finished within six months.
But according to new figures, which relate to the end of December, that target is not being met in many cases.
A total of 3,256 assessments were at least three months overdue at that point.
They include 812 children in the north Dublin region, along with 650 cases in Cork and Kerry.
Dr Martin Daly, a former president of the Irish Medical Organisation (IMO), says the figures are a disgrace.
"This is a reflection of a wider problem in the community in terms of access to services for children with disability.
"It reflects a waiting list for allied health professionals, for nursing professional assessments and also for needs assessments in terms of obtaining their rights under legislation."
The HSE acknowledges the numbers of assessments overdue for completion remain high.
But it says there has been some improvement over the past two years.
"The HSE is aware of the numbers of children waiting for assessments and therapy services and is fully cognisant of the stress this can cause to families."
Dr Daly said that vulnerable children are being badly let down.
"They are the silent minority and their voices often are not heard in their day-to-day stories and I think it is a sad reflection on our system that they are left in need for so long.
Their parents are struggling against all odds to provide services in their own homes at great cost to themselves and the State is falling short in their obligations to them.
Consultant psychiatrist Professor Patricia Casey said that the waiting lists are a disgrace.
"It's a very serious finding because these are children who are vulnerable educationally, they possibly have special needs in their education and yet they are missing out.
"So a child who is struggling at school and may need either assisted learning or even a special school will not be evaluated for this.
"It really is an appalling scenario."
According to Lorraine Dempsey from the Special Needs Parents Association, the numbers for the assessment of needs have gone up year by year.
"If we look back and take a snapshot of the previous year, at the end of 2018, there was 3,662 assessments that were overdue.
"So we have chipped away by about 400 but at the same time there are parts of the country that are massive blackspots."
