Hydraulic fracturing is a prospective technology for methane hydrate deposit exploitation. The evolution of hydraulically stimulated fractures around the point of liquid injection is simulated. For this purpose, the FLAC3D computer model is used because of its explicit calculation cycle that imitates real physics, prevents numerical instability, and reproduces a realistic path during simulation of the nonlinear rock massif behavior. The results of the simulation provide for new findings, namely, the spatial asymmetry and synchronism violation, spatial deviation, discontinuity, and recurrence during microseismic diffusion, which follow the process of hydraulic fracturing. In addition, dissipative structures were developed due to entropy production, since gas hydrate strata are an open thermodynamic system, which transforms and dissipates the energy of the injected liquid. The process of dissipative structure evolution should be controlled to enhance the gas yield from the hydrates.