In the following paper we present techniques for data-parallel execution of the Cellular Potts Model (CPM) on Graphics Processing Units (GPUs). We have developed data-structures and algorithms that are optimized to use available hardware resources on the GPU. To the best of our knowledge, this is the first attempt at using data-parallel techniques for simulating the CPM. We benchmarked this implementation against other parallel CPM implementations using traditional CPU clusters. Experimental results demonstrate that this implementation solves many of the drawbacks of traditional CPU clusters, and results in a performance gain of up to 30x, without sacrificing the integrity of the original model.