Preheat oven to 400°.
Arrange bones in an even layer in a shallow roasting pan. Bake at 400° for 45 minutes or until browned.
Transfer bones to an 8-quart stockpot. Add celery, carrot, tomato paste, and onions to pot; stir well to combine. Pour water over mixture; bring mixture to a simmer. Reduce heat, and simmer 5 hours, skimming surface occasionally.
Strain stock through a sieve into a large bowl; discard solids. Cool stock to room temperature. Cover and chill stock 8 to 24 hours. Skim solidified fat from surface; discard. Refrigerate remaining stock in an airtight container for up to 1 week or freeze for up to 3 months.