Forming conical parts is one of the complex and difficult fields in sheet metal forming processes. These parts are normally formed in industry by spinning, explosive forming or multistage deep drawing processes. In this paper, forming pure copper conical–cylindrical cups in the hydrodynamic deep drawing process was studied using finite element (FE) simulation and experiment. In this study, the effect of cone angle and punch tip radius on bursting and thickness distribution of the parts and also the effect of pressure path on thickness distribution were examined. Using the measurements of strains and thickness variations on the cup wall, the quality of the drawn cups was evaluated. The results demonstrated that increasing cone angle will lead to higher drawing ratio and uniform thickness distribution. Also, it was concluded that in the conical-cylindrical part the punch tip radius region is the most critical zone. At this zone, the more the cone angle the less the possibility of tearing is. In addition, with increasing punch tip radius it could be seen that the thickness reduction decreases.