Katsuji Yamashita is a supporting character in the series and one of the closest friends of the protagonist, Taison Maeda. He is easily recognized by his distinctive punch perm hairstyle and has a well-known insecurity regarding his broad forehead, which causes him to react with explosive anger whenever anyone mentions it. His family background is tied to a motorcycle repair shop run by his father, a business that Katsuji is expected to inherit and eventually does take over as a family trade. Despite his delinquent image, he has a sense of familial duty, acknowledging that his parents allowed him considerable freedom and that taking over the shop is his way of repaying them, even though he personally has other ambitions. In a moment that reveals a more gullible side, he initially believes his father's claim that the shop dates back to the year 1601, not stopping to consider that motorcycles did not exist then.

Katsuji's role in the story is firmly established as a loyal and integral member of the core friend group, forming a tight trio with Taison Maeda and Yoneji Sawamura. His friendship with Yoneji predates his encounter with Maeda, as they have known each other since elementary school. Their relationship began antagonistically when Katsuji, feeling threatened by Yoneji's academic and artistic abilities, bullied him. This conflict eventually led to a physical fight and, through that process, they became close friends, acting as a formidable duo throughout middle school. The pair first met Maeda during those middle school years after they accidentally provoked a man with yakuza connections. When the yakuza came to retaliate, Maeda intervened and helped them, and the three have been bound by a strong sense of chivalry and friendship ever since. This loyalty is a defining trait, as they often become involved in the numerous fights and gang conflicts that surround Maeda at Teiken High School.

Regarding personal relationships, Katsuji is in a long-term, tumultuous romance with a girl named Kazumi Imai. Their relationship is defined by constant bickering and accusations of infidelity, but it is serious enough that they eventually get married by the end of the series. His friendship with Maeda has a practical and humorous dimension as well. Because Katsuji works at his father's shop, Maeda often asks him to repair his motorcycle, and in lieu of payment, he lends Katsuji adult videos.

In terms of abilities, Katsuji is presented as a capable fighter, a necessary skill for surviving the violent world of the series, and he is shown to be skilled in the hands-on work of motorcycle repair and even engraving. He does not undergo a dramatic personality transformation but shows a grounded sense of responsibility as he accepts his future running the family business. Throughout the series, he remains a steadfast and reliable, if hot-headed, friend who contributes significantly to the group's dynamic as a loyal companion to Maeda and Yoneji.