Formations containing gas hydrates are encountered both during ocean drilling for oil or gas, as well as gas hydrate exploration and exploitation. Because the formations are usually permeable porous media, inevitably there are energy and mass exchanges between the water-based drilling fluids and gas hydrates-bearing formation during drilling, which will affect the borehole’s stability and safety. The energy exchange is mainly heat transfer and gas hydrate dissociation as result of it. The gas hydrates around the borehole will be heated to decomposition when the drilling fluids’ temperature is higher than the gas hydrates-bearing formation in situ. while mass exchange is mainly displacement invasion. In conditions of close-balanced or over-balanced drilling, the interaction between drilling fluids and hydrate-bearing formation mainly embodies the invasion of drilling fluids induced by pressure difference and hydrate dissociation induced by heat conduction resulting from differential temperatures. Actually the invasion process is a coupling process of hydrate dissociation, heat conduction and fluid displacement. They interact with each other and influence the parameters of formation surrounding the borehole such as intrinsic mechanics, pore pressure, capillary pressure, water and gas saturation, wave velocity and resistivity. Therefore, the characteristics of the drilling fluids invading into the hydrate-bearing formation and its influence rule should be thoroughly understood when analyzing on wellbore stability, well logging response and formation damage evaluation of hydrate-bearing formation. It can be realized by establishing numerical model of invasion coupled with hydrate dissociation. On the assumption that hydrate is a portion of pore fluids and its dissociation is a continuous water and gas source with no uniform strength, a basic mathematical model is built and can be used to describe the dynamic process of drilling fluids invasion by coupling Kamath’s kinetic equation of heated hydrate dissociation into mass conservation equations.