This thesis investigates minimal surfaces in design and researches their potential for constructability in concrete through the creation of physical prototypes with the design of two mold making processes, one being sacrificial and the other reusable. The study starts by acknowledging that minimal surfaces have been extensively explored in the field of differential geometry for decades. In spite of the availability of geometric definitions which provide the basic background for digital model generation (which in this text is assumed to be equal to design itself), minimal surfaces inspired very few people in their architectural design. This study attempts to look into the wider implications of minimal surfaces for architecture by taking up the challenge of designing and realizing various processes of mold making for the fabrication of such surfaces in concrete. Throughout this study, a gradient of complexity in the definition and digital modeling of minimal surfaces will be included as well as a variety of production methods in a research and fabrication based process, in order to investigate the correlation between what can be designed and what can be produced. I shall begin with a historical survey of the constructability of surfaces in thin shell concrete to provide background information for the reader. This chapter on the evolution of concrete structures presents a compilation of selected projects to illustrate the progress of thin shell construction throughout the history of architecture. It is here that I review what happened, why, and who made it possible. I draw heavily on published scholarly studies as most of the selected projects are cornerstones of the evolution of architecture and have been discussed by many others. Here, I simply attempt to remind the reader of the achievements of these projects in order to justify why investigation of the constructability of minimal surfaces may be the next step in the evolutionary process. After this section, the mathematics of surfaces in the complex plane is discussed based on information retrieved from many excellent resources. Here, the intention is to acquire information related to descriptions of various minimal surface types in differential geometry in order to be able to generate their representations in the digital environment. It would have been impossible to generate digital representations of minimal surfaces without the knowledge acquired through these descriptions. The last section provides a comparison of ruled surfaces and minimal surfaces meant to reveal the similarities and differences of such surfaces with regard to the principles of digital representation and fabrication. It provides insight into various fabrication techniques and materials to illuminate the design of a making process in which the goal is to know and control every parameter regarding both the design and fabrication of an object. The discussion of the design of a making process for a complexly shaped object provided in this part is followed by discussion of casting prototypes in concrete. In that section, the subject matter is the design and testing of various mold making techniques for the production of concrete prototypes of a selected minimal surface geometry. This section presents an increasing complexity of mold making from a sacrificial mold to a reusable mold.