In a shallow bowl, mix the flour, salt, and pepper. Lightly coat the round steak pieces in the flour mixture.
Heat the oil in a skillet over medium heat, and saute the celery, onion, and carrots about 5 minutes, until tender. Remove from heat, and set aside. Mix in the round steak pieces, and cook until lightly browned.
Place the vegetables and steak in a slow cooker. Mix in the tomatoes with juice, Worcestershire sauce, and brown sugar.
Cover, and cook 8 to 10 hours on Low, until the round steak is very tender.