The principal objective of research on the seismic properties of reservoir rocks is to develop a basic understanding of the effects of rock microstructure and its contained pore fluids on seismic velocities and attenuation. Ultimately, this knowledge would be used to extract reservoir properties information such as the porosity, permeability, clay content, fluid saturation, and fluid type from borehole, cross-borehole, and surface seismic measurements to improve the planning and control of oil and gas recovery. This thesis presents laboratory ultrasonic measurements for three granular materials and attempts to relate the microstructural properties and the properties of the pore fluids to P- and S-wave velocities and attenuation. These experimental results show that artificial porous materials with sintered grains and a sandstone with partially cemented grains exhibit complexities in P- and S-wave attenuation that cannot be adequately explained by existing micromechanical theories. It is likely that some of the complexity observed in the seismic attenuation is controlled by details of the rock microstructure, such as the grain contact area and grain shape, and by the arrangement of the grain packing. To examine these effects, a numerical method was developed for analyzing wave propagation in a grain packing. The method is based on a dynamic boundary integral equation and incorporates generalized stiffness boundary conditions between individual grains to account for viscous losses and grain contact scattering.