Abstract. Advanced accelerator research is aimed at finding new technologies that can dramatically reduce the size and cost of future high-energy accelerators. Supercomputing is already playing a dramatic and critical role in this quest. One of the goals of the SciDAC Accelerator Modeling Project is to develop code and software that can ultimately be used to discover the underlying science of new accelerator technology and then be used to design future high-energy accelerators with a minimum amount of capital expenditure on large-scale experiments. We describe the existing hierarchy of software tools for modelling advanced accelerators, how these models have been validated against experiment, how the models are benchmarked against each other, and how these tools are being successfully used to elucidate the underlying science.