Position Based Dynamics (PBD) is a popular approach used for animating constrained particle systems representing soft bodies, rigid bodies, and fluids. In this article, we present a massively parallel implementation of PBD for fast, interactive animation of deformable bodies. We divide the set of constraints in independent partitions using a fast, greedy coloring graph algorithm. Then, during the animation, the constraints belonging to each partition are solved in parallel on the GPU. We employ an efficient simulation pipeline using a memory layout that favors both the memory access time for computation and batching for visualization. Our experiments show that the achieved performance speed-up is several orders of magnitude faster than its serial counterpart.