This thesis describes the implementation of an implicit steady state solution method in the coupled TRAC/RELAP Advanced Computational Engine (TRACE) thermal-hydraulics system code and Purdue Advanced Reactor Core Simulator (PARCS) code with the goal of improving solution stability and efficiency. The implicit steady state solution method has been implemented within the framework of the existing pseudo-transient solution method in TRACE and includes time-dependent thermal-hydraulic and heat transfer equations and time-independent criticality neutron diffusion equations. The implicit steady state solution was first evaluated using two different meshes overlaid on a two-phase pipe model closely matching a boiling water reactor hydraulic channel. The two-phase pipe model showed that the implicit solution method reproduces the correct steady state solution for varying time step sizes for each mesh. A four-channel reactor model was created to further evaluate the performance of the implicit steady state solution. The results from the four-channel reactor model show that the computer runtime required in the implicit solution method is much greater than the required runtime for the well-developed and optimized explicit solution method. These results direct future development of the implicit solution method towards optimization strategies to reduce computer runtime.