Simultaneous measurements of compressional and shear wave speeds through polycrystalline methane hydrate have been made. Methane hydrate, grown directly in a wave speed measurement chamber, was uniaxially compacted to a final porosity below 2%. At 277 K, the compacted material had a compressional wave speed of 3650 ?? 50 m/s. The shear wave speed, measured simultaneously, was 1890 ?? 30 m/s. From these wave speed measurements, we derive V(p)/V(s), Poisson's ratio, bulk, shear, and Young's moduli.