Strengthening the upper arm, forearm, shoulders and chest muscles allows for a harder punch to be thrown. The back muscles play a part in how hard of a punch is thrown as well.
The triceps are a group of three muscles on the back of the upper arm. These muscles help to drive the arm forward. They are responsible for extension as the arm is extended for a punch, and once the punch is landed, they engage to keep the arm steady and solid against the surface. The wrist and the forearm contain a variety of muscle working together when punching. The flexor capris, flexor digitorum, palmaris longus, pronator teres and the brachioradialis work to keep the wrist straight and absorb the pressure from the punch to prevent the wrist from buckling and twisting under the force.
The majority of the power in a punch comes from the large muscles in the shoulder and the chest. The large muscle groups behind the force in a punch are the deltoid muscles, trapezius muscles and the pectoral muscles. When throwing hook and uppercut punches, the large muscle in the back, known as the latissimus dorsi, engages and adds power to the punch. It helps to push your punch forward and towards the intended object.