The duke said he wanted his children to be able to express their feelings.
Prince William's comments come after Prince Harry revealed he had sought counselling after spending nearly 20 years "not thinking" about the death of their mother, Diana, Princess of Wales.
Prince Harry has been praised for speaking out by the prime minister and mental health charities.
Prince William also highlighted the importance of people speaking out about their mental health in a video call with Lady Gaga.
The pair chatted about how important speaking freely on mental health problems can help shatter the stigma around them.
Prince William's comments on the "stiff upper lip" came in an interview - alongside Prince Harry - with a magazine produced by the charity Campaign Against Living Miserably (Calm), which is dedicated to preventing male suicide.
The future king and his brother are using the intense interest they generate to focus attention on a cause they are increasingly passionate about, BBC royal correspondent Peter Hunt says.
Prince William talked about his "tipping point", which was his exposure to suicide - the biggest killer of men aged under 45 in the UK - through his work as an air ambulance pilot.
He told Calm that while there might be a time and a place for the "stiff upper lip", it should not be at the expense of people's health.
The duke highlighted the importance of role models opening up about their mental health, including grime artist Stormzy.