Six defendants were sentenced to 20 years, 12 to 10-year terms, 12 others were given seven years and one was jailed for one year.
Judge Hilal bin Hamad Busaidi, who heads the state security court, said the defendants could not appeal the verdict, but could ask for a pardon from Oman's ruler, Sultan Qaboos bin Said Al Said, within 30 days.
The group's lawyers had said their clients were innocent and that they had merely sought to promote the setting up of Islamic clerical rule in Oman.
They said their clients' possession of weapons was in keeping with Omani norms, and that the worst they could be accused of was holding firearms without a permit.
The trial opened two weeks ago after the arrest of the accused in January.
The 31 defendants to stand trial were among as many as 100 suspected extremists arrested across Oman earlier this year, after unconfirmed reports some had planned to attack events at a popular shopping and cultural festival.
Officials have said many of those arrested were released.
Up to 200 supporters of the group marched in Muscat on Sunday demanding their acquittal.