Children with Osteogenesis Imperfecta (OI) have bone pain, low bone mass and fractures. There are no approved drugs for the treatment of OI in children, even though some intravenous (IV) bisphosphonates are used off-label in some countries. In a single dose, pharmacokinetic study, data showed that risedronate was well tolerated in 28 children with OI. This three year study will test the safety and efficacy of risedronate in the treatment of children with OI. For the first year, patients will be randomized to the risedronate and placebo groups in a 2:1 ratio. For the second and third years of the study, all patients will receive risedronate.