Methane (CH4) is the most abundant hydrocarbon and a significant greenhouse gas in the atmosphere. As earth's climate change is closely related to the global carbon cycle, understanding the processes affecting the dynamics of greenhouse gas CH4 in muddy aquatic sediments is particularly important. Effective elastic and physical properties of gas-charged sediments significantly differ from those of gas-free sediments, which makes gas to be distinguishable by using underwater remote acoustic technologies. By today, CH4 bubbles in the aquatic muds have been characterized at a micro-scale focusing on single bubble descriptors, but at macro-scale focusing on cumulative volumetric gas content only, while neglecting the bubble descriptors. None of the former works, however, are comprehensive enough to upscale the micro-scale gassy sediment descriptors, bubble size distribution, their orientations, inner bubble pressures, and cumulative bubble gas content, to the effective medium mechanical properties of gassy sediments. In this study, effective media theory is being developed to approximate the macroscopic mechanical properties of gassy aquatic muds. At a first stage of the project, single bubble descriptors are verified as functions of mechanical characteristics of gas-free ambient sediment: i.e., bubble semi-height, a, indicates a proportionality to Mode I Fracture Toughness, and normal crack opening displacement at any point of the growing buoyant bubble surface depends explicitly upon Young's modulus. Results of the conducted simulations demonstrated a good agreement with analytical predictions. A Gaussian bubble size distribution pattern is designed in the representative elementary volume, attributed to different bubble growing stages, from bubble nucleation to its mature configuration, while the maximum bubble sizes are controlled by sediment mechanical properties. Sound speed, attenuation, and other dependences of acoustic characteristics of gassy sediment on the micro-scale bubble descriptors are being elaborated, modelled by geoacoustic inversion technique. Suggested effective medium modelling will enhance the accuracy of the acoustic data processing and will introduce the additional possibilities of capturing the important in-situ CH4 bubbles descriptors in the aquatic muds.