Mix flour, 1/2 teaspoon salt, and 1/4 teaspoon black pepper together in a bowl. Sprinkle half the flour mixture on one side of round steak pieces; pound steak until coating is absorbed. Flip steak and coat with remaining flour mixture; pound steak until coating is absorbed. Cut steak into 6 pieces.
Melt shortening in a large skillet over medium heat; place steak pieces in the hot shortening. Cook until browned, 7 to 10 minutes per side. Cover and simmer until tender, about 1 hour, adding water as needed.
Turn steak pieces over and add tomatoes, onion, and green bell pepper to the skillet. Season with salt and black pepper. Simmer until vegetables are tender, about 30 more minutes.