Abstract Invasion of mud filtrate from the borehole into the surrounding formation can significantly alter the response of logging tools. In this paper the neutron tool response was calculated for a gas-bearing rock crossed by the borehole. The invaded zone is characterized by variable fluid and gas saturation and is defined by a specific hyperbolic function. The saturation function is based on the characteristics of Polish Carpathian Foredeep Miocene formations reached in gas-bearing rocks. The whole system including neutron tool equipped with Am-Be neutron source and a set of neutron detectors, borehole, invaded zone, and virgin zone, was numerically modeled and used as the input to the Monte-Carlo neutron transport code. The response of each detector was calculated for different combinations of porosity and saturation of invaded zone and virgin zone.