The coal mass deformation and fluid flow coal-bed methane and water two phases fluid flow in coal bed interact during coal-bed methane exploitation. Because of coal-bed methane adsorption and de-sorption, coal-bed methane flow is an an-isothermal procedure. In this paper, the coal skeleton is assumed to have elastic-plastic behavior, the deformation equations were derived and according to the elasto-plastic theory. Based on the Darcy's law, and considered the coal-bed methane adsorption and de-sorption effect the author erected mathematical models for coal-bed methane and water flow through co...