In this paper, we present results of using high-performance parallel computers to simulate beam dynamics in an early design of the Spallation Neutron Source (SNS) linac. These are among the most detailed linac simulations ever performed. The simulations have been performed using up to 500 million macroparticles, which is close to the number of particles in the physical system. The simulations are fully three-dimensional, and utilize RF cavity field data from modeling over 400 RF cavities. Furthermore, they use an improved model of the beam dynamics within the cavities. Traditionally, small-scale two-dimensional simulations have been performed on PCs or workstations. While such simulations are sufficient for rapid design and for predicting root mean square properties of the beam, large-scale simulations are essential for modeling the tails of the beam. The large-scale parallel simulation results presented here represent a three order of magnitude improvement in simulation capability, in terms of problem size and speed of execution, compared with typical two-dimensional serial simulations. In this paper we will show how large-scale simulations can be used to predict the extent of the beam halo and facilitate design decisions related to the choice of beam pipe aperture.