Thick sheet punching is a process used in the automobile industry, especially in the heavy vehicles segment. Aimed at generating holes of good cylindricity and surface quality, the definition of the process parameter values and the tool design are critical to the process. For this purpose, the finite element method is useful to decrease the trial-and-error procedures and also the tool development costs. The main aim of the present study was to analyse the influence of the punch design on the final quality of punched/broached holes produced on thick steel sheets (8 mm, NBR 6656). Several geometries of punch with combined broaching teeth as well as punches with traditional geometries have been analysed. The results of the simulations led to a detailed understanding of the influence of punch geometry during the punching–broaching process. In addition, a novel punch design approach was proposed which allowed the production of holes of good cylindricity due to the progressive variation of the clearance between the punch and the die during the punch penetration progress.