POLICE arrested six young pro-independence demonstrators in Lhasa yesterday and the city remained tense following a major anti-Chinese protest early last week, according to tourists. Six youths, apparently in their late teens, ran across Barkhor Square in the heart of the regional capital at about noon waving Tibetan flags. Police apprehended them within minutes, bundled them into trucks and took them away. ''They were caught within a minute or two, and beaten with sticks,'' said one Western source. ''As soon as one got caught, the others came running in.'' The source said Tibetan-run shops were closed for the Saga Dawa festival marking the Buddha's birthday yesterday. The Jokhang, the holiest temple in Tibet, was full of worshippers. About 20 riot police were in the square. ''But there were tons of undercover plain-clothes police patrolling the city,'' a witness said. The atmosphere was tense. ''Any loud noise, and people would turn around to see whether they should run,'' said a Western traveller. On May 24, hundreds of people demonstrated against Chinese rule in the biggest protest since March 1989. Dozens of people have apparently been arrested since then.