Louise Erdrich's story "The Red Convertible" features both round and flat characters as well as some that are simply stock (or representative or stereotype) characters. Let's define these terms and look at examples from the story.
A round character has a fully developed personality, participates in conflicts with other characters, and often changes throughout the story. The brothers Henry and Lyman are both round characters. They are explorers, adventurers, partners in travel, and best friends at the beginning of the story. Lyman has a knack for making money, and together, they buy a red convertible.
But then, Henry is drafted into the military and goes to Vietnam. He comes back a totally different man. Today, we would say that he probably has post traumatic stress disorder. He hardly talks and sits in front of the TV for hours on end until Lyman deliberately messes up the convertible so that Henry can fix it up again. The two brothers make one last trip together, get in a fight over the car, and end up laughing. Then Henry jumps into the river. His stress is too much for him. Lyman tries to save his brother but cannot, and he pushes the car in after him, not wanting to keep it. After his brother's death, Lyman has some stress and depression of his own.
The other characters in the story, like Susy, Bonita (the sister), and Henry and Lyman's mother are flat characters. They are not well developed and do not have conflicts or many personality traits of their own. They are merely there to serve the plot and the two main characters. Bonita is the stereotypical little sister. Susy is the pretty-girl stock character. The mother is just a placeholder mother and does and says very little.