The majority of presently exploitable marine methane hydrate reservoirs are likely to host hydrate in disseminated form in coarse grain sediments. For hydrate concentrations below 25–40%, disseminated or pore‐filling hydrate does not increase elastic frame moduli, thus making impotent traditional seismic velocity‐based methods. Here, we present a theoretical model to calculate frequency‐dependent P and S wave velocity and attenuation of an effective porous medium composed of solid mineral grains, methane hydrate, methane gas, and water. The model considers elastic wave energy losses caused by local viscous flow both (i) between fluid inclusions in hydrate and pores and (ii) between different aspect ratio pores (created when hydrate grows); the inertial motion of the frame with respect to the pore fluid (Biot's type fluid flow); and gas bubble damping. The sole presence of pore‐filling hydrate in the sediment reduces the available porosity and intrinsic permeability of the sediment affecting Biot's type attenuation at high frequencies. Our model shows that attenuation maxima due to fluid inclusions in hydrate are possible over the entire frequency range of interest to exploration seismology (1–106 Hz), depending on the aspect ratio of the inclusions, whereas maxima due to different aspect ratio pores occur only at sonic to ultrasound frequencies (104–106 Hz). This frequency response imposes further constraints on possible hydrate saturations able to reproduce broadband elastic measurements of velocity and attenuation. Our results provide a physical basis for detecting the presence and amount of pore‐filling hydrate in seafloor sediments using conventional seismic surveys.