The production of paperboard packaging components in fast-running machines requires reliability of the production process. Boundaries for the process parameters and constraints for the geometry of the tools require investigation to determine dependable configurations. This paper aimed to investigate the relationships between process parameters, tool geometry, and the occurrence of rupture in the deep-drawing process of paperboard. Different types of ruptures in various phases of the process were distinguished and linked to their specific cause. An extensive experimental investigation with multiple variables of influence was conducted. A logistic regression model was used to describe the experimental data and was statistically validated. The blankholder force was found to be the most influential parameter. Interactions between the parameters blankholder force, punch velocity, and punch diameter were recognized. A high punch velocity can reduce the probability of rupture when the punch diameter is adjusted.