Oregon State University (OSU) has developed and patented a technology that produces 99Mo within a standard TRIGA reactor core and does not negatively impact safety bases for the operations of such reactor designs. This new technology, referred to as the “molybdenum element,” is intended on being demonstrated within the OSU TRIGA Reactor (OSTR) with figures of merit including 99Mo yield and operation. A comprehensive design and thermal-hydraulic analysis has been conducted to characterize the safety-related traits of the molybdenum element to facilitate a license amendment through the U.S. Nuclear Regulatory Commission to insert such an experiment in the OSTR. This study details the thermal-hydraulic characteristics of the molybdenum element exhibited within the OSTR under the three sets of conditions necessary to demonstrate the element's safety. The study leverages the lumped-parameter code RELAP5-3D Version 2.4.2 for conduct of the primary body of this work. The first condition analyzes the molybdenum element's response under steady-state, full-power operation; the second condition assumes that the inner region of the annular molybdenum element is blocked while remaining at full power; and the last condition considers several loss-of-coolant-accident scenarios. Key thermal-hydraulic parameters that may impact the safety of the OSTR are identified, presented, and discussed herein. The result of this study provides objective evidence through use of RELAP5-3D that the molybdenum element remains in a safe state during the steady and abnormal conditions considered.