This paper presents new analytical model of gas-water flow in coal seams in one dimension with emphasis on interactions between water flowing in cleats and coal matrix. Coal as a flowing system, can be viewed as a solid organic material consisting of two flow subsystems: a microporous matrix and a system of interconnected macropores and fractures. Most of gas is accumulated in the microporous matrix, where the primary flow mechanism is diffusion. Fractures and cleats existing in coal play an important role as a transportation system for macro scale flow of water and gas governed by Darcy’s law. The coal matrix can imbibe water under capillary forces leading to exchange of mass between fractures and coal matrix. In this paper new partial differential equation for water saturation in fractures has been formulated, respecting mass exchange between coal matrix and fractures. Exact analytical solution has been obtained using the method of characteristics. The final solution has very simple form that may be useful for practical engineering calculations. It was observed that the rate of exchange of mass between the fractures and the coal matrix is governed by an expression which is analogous to the Newton cooling law known from theory of heat exchange, but in present case the mass transfer coefficient depends not only on coal and fluid properties but also on time and position. The constant term of mass transfer coefficient depends on relation between micro porosity and macro porosity of coal, capillary forces, and microporous structure of coal matrix. This term can be expressed theoretically or obtained experimentally.