NSPCC Cymru said just two children were reported to North Wales Police in 2013, rising to four in 2014 then 28 in 2015.
Most of those reported - 24 - were aged 15 or under while 10 were 16 or 17.
Des Mannion, head of service at NSPCC Cymru said: "It is very worrying that more children are sharing explicit images of themselves."
He added: "Although the figures in north Wales are relatively small, the fact that there has been a sharp increase in the number of cases reported to police is a concern."
The NSPCC wants children to be warned about the dangers of sexting through compulsory online safety lessons and wants to see the next Welsh Government implement a plan for this.
While the majority of these types of images were shared via mobile phones, they were also sent using apps such as Snapchat, Instagram and Facebook.
Mr Mannion added: "We are very concerned that children are putting themselves at risk of exploitation or bullying in this way.
"Children need to be taught about the dangers of sexting and how the consequences can be devastating if they lose control of an image."
In February, police in England and Wales began producing new guidelines designed to avoid "criminalising" children caught sending indecent images to each other.

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The deal will keep the Ivory Coast international at the Etihad Stadium until 2017.
"This is where I want to be," the 29-year-old told the club website.
"I will never forget how I have been treated here by the fans, the club and the owners and nothing would give me greater pleasure than to finish my career as a Manchester City player."
Toure joined City from Barcelona for a reported £24m in 2010, having helped the Spanish giants win the Champions League title a year earlier.
The box-to-box midfielder has since been an integral member of Roberto Mancini's side, scoring the winning goal in the 2011 FA Cup final and a crucial double against Newcastle United last May to keep the eventual Premier League champions in the title hunt.
We must try to finish on a high note and then start preparing to win more next season
Toure has scored eight goals this season as City have progressed to a Wembley FA Cup semi-final against Chelsea on Sunday 14 April, but his side made an early Champions League exit and are 15 points behind Manchester United in the league with only seven games remaining.
"Of course now it looks likely that we will not successfully defend the Premier League title and that is sad for all of us," Toure added. "But we can still finish second and win the FA Cup for a second time in three years and that is still an achievement for a club that won nothing for a long time.
"We must try to finish on a high note and then start preparing to win more next season. Football is always a challenge and always a puzzle to solve and that is why we all love the game.
"You have to use your skill, intelligence and strength to constantly improve and that is what we at City intend to do."
A rise in under-18s being reported to the police for distributing indecent images of children has raised concerns over 'sexting'.
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An ex-England captain, a former Lance Bombardier in the Army and the most expensive signing in Championship history.
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Manchester City midfielder Yaya Toure has signed a new four-year contract with the Premier League club.