The lack of opportunities to perform his work or watch live productions risks marginalising the world's best-known playwright for a generation of children, said Maria Evans, the RSC's director of learning.
Her comments come as the RSC launches a major campaign calling for every child in the UK to see at least one compulsory performance of a Shakespeare play during their school life.
It also wants theatre-based activities to form part of English lessons and a practical element added to examinations, which it says focus too heavily on memorising lines without proper understanding of their significance.
Shakespeare is currently the only author who must be studied as part of the national curriculum.
But writing in The TES today, Ms Evans said: "Stop your average young person in the street and ask them about Shakespeare and you can guarantee that 'boring' will be a fairly common response.
"Shakespeare remains the only writer studied by every young person in the country, but many leave formal education determined never to come into contact with the Bard again."
Currently 11 to 14-year-olds in Wales are required to study at least one of the Bard's plays, but the choice is left to their schools. They must also study Shakespeare at GCSE, where the text is determined by the exam board.
Ms Evans said there was concern that written key stage 3 tests in England were a turn-off for children and did nothing to encourage theatre-based productions of Shakespeare's plays. KS3 tests are now optional in Wales and will disappear in 2008.