Place the beef pieces between sheets of plastic wrap and pound them to about 1/2 inch thick with a meat mallet.
Mix the flour, salt, and pepper in a shallow dish. Dredge each piece of beef in the flour mixture, shaking off excess.
Heat the vegetable oil in a large skillet over medium-high heat. Brown the beef on both sides, about 3 minutes per side, then remove to a plate.
Add the sliced onions to the same skillet and cook until they soften, about 5 minutes.
Stir in the diced tomatoes and beef broth, scraping the bottom of the skillet to loosen any browned bits.
Return the beef to the skillet, spoon some sauce over the top, and bring the mixture to a simmer.
Cover the skillet, reduce the heat to low, and cook for 1 hour until the beef is fork-tender.
Serve the Swiss steak and sauce over the cooked white rice.