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Presence of open fractures in a fluid-saturated porous rock causes significant attenuation and dispersion of seismic waves due to wave induced fluid flow between pores and fractures. We present an analytical model for attenuation and dispersion of compressional waves in a porous rock with a periodic system of aligned fractures using the theory of elastic wave propagation normal to layered porous media. Numerical simulations are then performed through the use of OASES reflectivity code with both periodic and random fracture distributions being modeled.