The Finite Element Method is a computationally expensive method used to perform engineering analyses. By performing such computations on a parallel machine using a SIMD paradigm, these analyses' run time can be drastically reduced. However, the mapping of the FEM mesh elements to the SIMD machine processing elements is an NP-complete problem. This thesis examines the use of Genetic Algorithms as a search technique to find quality solutions to the mapping problem. A hill climbing algorithm is compared to a traditional genetic algorithm, as well as a "messy" genetic algorithm. The results and comparative advantages of these approaches are discussed.