Tensor decompositions have gained popularity in various research communities as a means of analyzing high dimensional, complex data. Generalizations of matrix decompositions to more than 2 dimensions, tensor decompositions are useful in machine learning, chemometrics, computer vision, graph analysis, and other areas/applications. The focus of this Masters Thesis is the Canonical Polyadic or CP Decomposition for dense tensors. We discuss and present shared and distributed memory parallel algorithms for computing a CP Decomposition and explore a motivating neuroimaging application. Our implementations scale to hundreds of nodes and thousands of cores on distributed memory machines. We obtain up to 2x speed up over state of the art software, and demonstrate the CP's utility in revealing latent pattern in data via a neuroimaging application.