Place flour on a large plate and set aside. Cut round steak into serving pieces. Salt & pepper as desired. Dredge steak in flour (really press in well), use a meat mallet to pound the meat. Repeat this pounding process on both sides until the meat is about 1/2 inch thick and noticeably more tender. Add a bit more flour if it becomes sticky.
Heat vegetable oil in a large ovenproof skillet over medium heat; cook the onions, green peppers and garlic for 5 minutes. Add the floured beef to the pan, pushing vegetables to one side. Brown until the meat is golden brown, turning once. This will likely have to be done in batches.
Place meat in the bottom of a 3 quart baking dish. Cover the meat with the onion mixture, then the tomatoes. Add a little water if needed.
Cover tightly and place in oven until done, about 1 to 1 1/2 hours. Remove meat, stir sauce and vegetables together and serve with meat.