Methane gas hydrates have attracted significant international interest due to their potential as a future energy resource, but also as a geotechnical hazard for offshore operations related to hydrocarbon recovery. In this context, the ability to detect and quantify the presence and concentration of hydrate in submarine sediments and understand the effects it has on host sediments has become increasingly important. Detection and quantification of gas hydrates has been inferred via exploratory seismic surveys, which measure indirectly the bulk dynamic properties of sizeable volumes of sediment in situ. Seismic data are then interpreted using an effective medium model, which employs theoretical assumptions to relate wave velocities to gas hydrate content of the sediment. Wave velocity can then be used to infer hydrate concentration levels. Methane gas hydrates occur in situ in a variety of sediments ranging from coarse-grained sands to fine-grained clays and silts, each hosting a variety of morphologies which occur as two basic types, pore-filling and grain-displacing. There are effective medium models for pore-filling morphologies while there is a lack of modeling techniques that consider grain-displacing morphologies and their effect on the physical properties of gas hydrate-bearing sediments. Thus the effect of hydrate morphology on submarine sediments is poorly understood. A numerical modeling approach, based on computational homogenization that has not been applied as yet for gas hydrate-bearing sediments is presented. The approach considers the multi-scale nature of the material from a geotechnical engineering perspective and has the ability to represent material geometry explicitly. The effect of hydrate on the overall seismic properties of the host sediment is portrayed through simulations of nodular and simple vein morphologies with differing hydrate contents. Results show that morphology has a significant effect on the overall material properties, with the effect being more pronounced on the overall compression wave velocity than on the overall shear wave velocity. The ratio of the two velocities (V_p/V_s) differs depending on the type of morphology and can provide insight into the underlying morphology by assisting in the differentiation between nodular and vein morphologies.