After a decade of experience, the Stockpile Stewardship Program continues to ensure the safety, security and reliability of the nation's nuclear weapons. The Advanced Simulation and Computing (ASCI) program was established to provide leading edge, high-end simulation capabilities needed to meet the program's assessment and certification requirements. The great challenge of this program lies in developing the tools and resources necessary for the complex, highly coupled, multi-physics calculations required to simulate nuclear weapons. This paper describes the hardware and software environment we have applied to fulfill our nuclear weapons responsibilities. It also presents the characteristics of our algorithms and codes, especially as they relate to supercomputing resource capabilities and requirements. It then addresses impediments to the development and application of nuclear weapon simulation software and hardware and concludes with a summary of observations and recommendations on an approach for working with industry and government agencies to address these impediments.