Northumbria Police said the pair were arrested on suspicion of possessing indecent images.
A spokesman said investigations were ongoing to "ensure the safeguarding of those involved" and to check that there was no ongoing risk of exploitation.
Both boys have been bailed pending further inquiries.
Supt Sarah Pitt said the force was working with schools across South Tyneside to make children "aware of the risks around sharing images of themselves and others via text and social network sites".
She said: "The internet is an essential tool and social networking sites are a popular way for children to communicate with their friends, but we need to make sure they stay safe online and know how to use it responsibly.
"It's very important that we make sure young people stay safe online and are aware of the risks and what they can do to avoid them.
"Anyone who may have concerns about images they have shared or received should speak with a trusted adult or the police straight away."

Anna Jacobs read the description by Tecomak Environmental Services in an email inviting her for interview.
Attached seemingly by accident, the comments suggested Ms Jacobs, of Horsmonden in Kent, was "worth an interview if only for a laugh".
The company said it was investigating thoroughly but added the comments had been taken out of context.
Ms Jacobs told BBC South East Today she was initially excited to be invited for the interview for a position of office administrator.
But then she saw the "absolutely awful summary" and said she was "furious".
Below the formal invitation, the e-mail from Tecomak read: "Home educated oddball. Can't get a job since leaving uni. Forages for mushrooms.
"Difficult to assess from her CV - might be very good but equally could be a biscuit short of a packet or a left-wing loon tree hugger.
"Worth an interview if only for a laugh."
Ms Jacobs said she had a lot to offer and could not believe the firm was considering wasting her time for "a laugh".
So far, she said she has received no apology or explanation from Tecomak.
Employment lawyer Richard Atkins, said all jobseekers are entitled to equal treatment when applying for positions.
"On the face of it, this e-mail does not show that she has been treated with fairness and respect," he said.

Michael McGibbon, 33, died after an attack in an alleyway at Butler Place, with police saying his killing carried the hallmarks of a paramilitary murder.
The 34-year-old was arrested in Belfast on Sunday.
Mr McGibbon was married with a young family.
A priest, Father Gary Donegan, told the BBC's Sunday News programme how Mr McGibbon's wife tried to save his life when she arrived at the scene.
Mrs McGibbon, who is a nurse, came to his aid shortly after the shooting.
Police have said Mr McGibbon had contacted them to inform them that two masked men had arrived at his house on Thursday evening.
The men asked him to come out of the house but he refused, and they told him they would return.
Mr McGibbon's murder had been referred to the Police Ombudsman for Northern Ireland.
Two schoolboys aged 12 and 13 have been arrested after concerns were raised about children sharing inappropriate images on social media.
[NEXT_CONCEPT]
A graduate jobseeker has spoken of her horror at being called a "home-educated oddball" by a prospective employer.
[NEXT_CONCEPT]
A 34-year-old man is still being questioned over the murder of a man who was shot in the legs in north Belfast on Friday night.