Transient wave propagation in granular materials is numerically studied using discrete element simulation. Three particular cases are investigated including dry cohesionless material, elastic cemented particulate media and fluid saturated granular material. Primary interest is concerned with linking material microstructure with wave propagational behaviors. The discrete element scheme uses several different inter-particle contact laws appropriate to the material modeling application. Simulation results yield information on wave speed and amplitude attenuation for two-dimensional, meso-domain model assembly systems of circular disks and spherical particles. Particulate models were numerically generated using a biasing scheme whereby partial control of particular fabric measures could be achieved. Particular fabric measures which were used to characterize the granular material models include branch and cementation vectors. Discrete element modeling (DEM) wave simulation results indicated that wave speed is dependent upon the stiffness of the interparticle contacts and distribution of branch vectors along the propagation direction. Wave amplitude attenuation is also dependent on the number of branch vectors in the direction of propagation.