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In this research, we have attempted to characterize the anisotropy in particle arrangement and particle interactions that develop when a granular material is deformed and to determine the influence of this anisotropy on the subsequent behavior of the material. The research has dealt with the behavior of an idealized granular material consisting of lass spheres and has involved the close interaction between physical experiments, numerical simulations, and the development of theory. We have focused on: (1) Understanding the relationship between the developing anisotropy of the material and the changes in volume observed in deformations in which the mean stress is held constant. In particular, we have considered the volume change of a hollow cylindrical sample in triaxial compression and extension; (2) Using elastic waves to probe the evolution of the internal structure of the granular material as it is being deformed; and (3) Developing constitutive relations for general stress paths in the triaxial/torsional device through the combined efforts of theoretical modeling and numerical simulation.