To assure nuclear power sustainability, ongoing efforts on advanced closed-fuel cycle options and adapted open cycles have led to investigations of various strategies involving utilization of Transuranic (TRU) nuclides in nuclear reactors. Due to favorable performance characteristics, multiple studies are focused on transmutation options using High Temperature Gas-cooled Reactors (HTGRs). Prismatic HTGRs allow for 3-Dimensional (3D) fuel shuffling and prior shuffling algorithms were based on experimental block movement and/or manual block shuffle patterns. In this dissertation, a physics based 3D multi-directional reloading algorithm for prismatic deep burn very high temperature reactors (DB-VHTRs) was developed and tested to meet DB-VHTR operation constraints utilizing a high fidelity neutronics model developed for this dissertation. The high fidelity automated neutronics model allows design flexibility and metric tracking in spatial and temporal dimensions. Reduction of TRUs in DB-VHTRs utilizing full vectors of TRUs from light water reactor spent nuclear fuel has been demonstrated for both a single and two-fuel composition cores. Performance of the beginning-of-life and end-of-life (EOL) domains for multi-dimensional permutations were evaluated. Utilizing a two-fuel assembly permutation within the two-fuel system domain for a Single-Fuel vector, the developed shuffling algorithm for this dissertation has successfully been tested to meet performance objectives and operation constraints.