The Eastern Province, where Qatif is located, was the site of frequent Shiite-led protests between February 2011 and August 2012.
A specialised court in Riyadh yesterday sentenced the young defendants to between six and 20 years in prison and imposed travel bans of the same duration as their jail terms.
They were convicted of "taking part in protests", "chanting slogans against the state", and "possessing and making Molotov cocktails", according to local newspapers.
The defendants said they would appeal.
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Protests first erupted in the province of eastern Saudi Arabia, home to most of the kingdom's two-million-strong Shiite minority, in March 2011.
Since then 10 people have been killed in clashes with security forces.
Fighting intensified after the arrest in July 2012 of Sheikh Nimr al-Nimr, considered to be a driving force behind the protests.
However, tensions eased in August that year when seven Shiite dignitaries from Qatif hailed a call by King Abdullah for the creation of a centre for Sunni-Shiite interfaith dialogue.