Decomposition of Methane Hydrate is studied numerically. Global one-step irreversible reaction model is applied for melting Methane Hydrate and its Arrhenius type of temperature dependency. Two-dimensional, time-dependant phenomena in the cold Methane Hydrate block are simulated. As the time goes by, local temperature increases due to thermal conduction and then the decomposition of Methane Hydrate starts, which discourages the rise of the temperature because of the endothermic reaction.