Wash the short ribs and pat them dry with paper towels. Dredge the ribs in flour and place in a hot skillet with some oil. Brown the ribs on all sides.
Place the short ribs, 8 cups of water, onions, green pepper, celery, salt, and pepper in a heavy 6-qt pot. Heat over medium-high heat until boiling. Reduce the heat to simmering and simmer until the short ribs are tender, for about 1 1/2 to 2 hours. Move the short ribs to a bowl and keep warm.