Kate and William would get mental health support for their children if necessary
The Duke and Duchess of Cambridge "feel very strongly" about getting expert mental health support for their children if they needed it.
Kate, patron of the Anna Freud National Centre for Children and Families - a children's mental health charity - said getting early support for a child who is struggling to cope is "the best possible thing we can do".
The charity has launched a series of expert podcasts in a bid to help parents understand and manage child and family mental health problems.
Child In Mind, presented by BBC Radio 4 presenter Claudia Hammond, features 20-minute episodes in which an issue in child and family mental health is discussed with an expert and a young person or parent.
Kate, who works to raise awareness of mental health issues, said: "One in three adults still say they would be embarrassed to seek help for their child's mental health.
"No parent would fail to call the doctor if their child developed a fever, yet some children are tackling tough times without the support that can help them because the adults in their life are scared to ask. It doesn't need to be like this.
"Throughout my work with family and child support organisations, one thing that has stood out to me time and again is that getting early support for a child who is struggling to cope is the best possible thing we can do to help our children as they grow up.
"Knowing this, both William and I feel very strongly that we wouldn't hesitate to get expert support for George and Charlotte if they need it.
"I hope that this excellent series of podcasts by the Anna Freud Centre will go some way to help families overcome that fear of what happens next if they look for professional support.
"They illustrate that many of the therapies are actually very simple and practical steps that include the whole family to help children make sense of the world around them.
"They show how with the right help, children have a good chance of overcoming their issues while they are still young, and can have the bright future they deserve.
"Please do listen, and share them with your friends and family and let's change the way we all talk to each other about our mental health."
The first episode focuses on childhood anxiety and features Beckie, whose 10-year-old son Luke's anxiety caused severe difficulties in her family's life.
Beckie said: "I've always wanted to be a mum. However, along with delight and satisfaction, being a mum has also unearthed feelings of frustration and self-doubt. These feelings were particularly amplified by my eldest son's anxiety.
"This podcast is a great opportunity to share my experience with other parents so that they know that they are not alone."
Other episodes focus on topics including self-harm, ADHD, eating disorders, how the adolescent brain develops and what this means for parenting, the evidence for use of medication for child and teenage mental health problems, the science behind bonding with your baby, and what we know about the impact of sexual material online.