The problem of efficient parallelization of 2D Ising spin systems requires realistic algorithmic design and implementation based on an understanding of issues from computer science and statistical physics. In this work, we not only consider fundamental parallel computing issues but also ensure that the major constraints and criteria of 2D Ising spin systems are incorporated into our study. This realism in both parallel computation and statistical physics has rarely been reflected in previous research for this problem. In this thesis,we designed and implemented a variety of parallel algorithms for both sweep spin selection and random spin selection. We analyzed our parallel algorithms on a portable and general parallel machine model, namely the LogP model. We were able to obtain rigorous theoretical run-times on LogP for all the parallel algorithms. Moreover, a guiding equation was derived for choosing data layouts (blocked vs. stripped) for sweep spin selection. In regards to random spin selection, we were able to develop parallel algorithms with efficient communication schemes. We analyzed randomness of our schemes using statistical methods and provided comparisons between the different schemes. Furthermore, algorithms were implemented and performance data gathered and analyzed in order to determine further design issues and validate theoretical analysis. / Master of Science