The observation of neutrinoless double-beta decay would confirm the Majorana nature of the neutrino and would allow one to potentially determine the mass of neutrinos. The goal of the MAJORANA collaboration is to develop a tonne-scale Ge-76-based neutrinoless double-beta decay experiment. Currently, efforts are underway to construct the MAJORANA DEMONSTRATOR, a 44.8-kg array of germanium crystals, located at the 4850' level of the Sanford Underground Research Facility (SURF) in Lead, SD. The goal of the DEMONSTRATOR is to demonstrate the ability to construct a detector composed of an array of germanium crystals while maintaining an unprecedented low background that is essential for the observation of neutrinoless double-beta decay. Before the assembly and operation of the DEMONSTRATOR, a single test cryostat was built. This cryostat, referred to as the Prototype Cryostat, was built to test the clean assembly procedures that are to be used for the DEMONSTRATOR. Understanding the backgrounds of the MAJORANA DEMONSTRATOR is of the upmost importance and for this reason, much effort has been put into creating an accurate background model. While achieving the lowest possible background is the goal of the DEMONSTRATOR, this is not necessarily true of the Prototype Cryostat, whose main purpose is to improve on cryostat assembly procedures, analysis routines and the like. Nevertheless, understanding the backgrounds of the Prototype Cryostat can help to verify the background model of the DEMONSTRATOR. Thus a background model of the Prototype Cryostat has been developed using the same techniques that are being used to develop the background model of the DEMONSTRATOR. This dissertation discusses the development of the Prototype Cryostat background model, its successes and failures, and the implications for the DEMONSTRATOR.