Place rice and water in a medium-size pot. Bring water to a boil, when boiled reduce heat to a simmer, cover pot and let rice cook until tender.
In a large mixing bowl, combine red onion, celery, and cucumber. Crumble the feta into the bowl. Cover the vegetable mixture with cooked rice, cover and let sit for 5 minutes.
Toss vegetable and feta with oil and vinegar, and serve.