Mold design can be a difficult, time-consuming process. Determining how to split a mold cavity into multiple mold pieces (e.g., core, cavity) manually can be a tedious process. This paper focuses on the mold construction step of the automated mold design process. By investigating glue operations and its relations with parting faces, an approach based on a new reverse glue operation is presented. The key to the reverse glue operation is to generate parting faces. A problem definition of parting face generation for a region is provided. Correspondingly, three face generating criteria are identified. Based on the parting lines of a region, our algorithms to generate the parting faces are presented. Our mold construction algorithms for two-piece molds and multi-piece molds are also presented with brief discussions. Some industrial examples are provided which illustrate the efficiency and effectiveness of our approach. We tested our mold designs by fabricating stereolithography mold inserts (a rapid tooling method) and molding parts.