Digital rock methodology combines modern microscopic imaging with advanced numerical simulations of the physical properties of rocks. Modeling of elastic-wave propagation directly from rock microstructure is integral to this technology. We survey recent development of the rotated staggered grid (RSG) finite-difference (FD) method for pore-scale simulation of elastic wave propagation in digital rock samples, including the dynamic elastic properties of rocks saturated with a viscous fluid. Examination of the accuracy of this algorithm on models with known analytical solutions provide an additional accuracy condition for numerical modeling on the microscale. We use both the elastic and viscoelastic versions of the RSG algorithm to study gas hydrates and to simulate propagation of Biot's slow wave. We applyRSG method ology to examine the effect of gas hydrate distributions in the pore space of a rock. We compare resulting P-wave velocities with experimentally measured data, as a basis for building an effective-medium model for rocks containing gas hydrates. We then perform numerical simulations of Biot's slow wave in a realistic 3D digital rock model, fully saturated with a nonviscous fluid (corresponding to the high-frequency limit of poroelasticity), and placed inside a bulk fluid. The model clearly demonstrates Biot's slow curve when the interface is open between the slab and bulk fluid. We demonstrate slow wave propagation in a porous medium saturated with a viscous fluid by analyzing an idealized 2D porous medium represented alternating solid and viscous fluid layers. Comparison of simulation results with the exact solution for this layered system shows good agreement over a broad frequency range.