Landfill gas, originating from the anaerobic biodegradation of the organic content of waste, consists mainly of methane and carbon dioxide, with traces of volatile organic compounds. Pressure, concentration and temperature gradients that develop within the landfill result in gas emissions to the atmosphere and in lateral migration through the surrounding soils. Environmental and safety issues associated with the landfill gas require control of off-site gas migration. The numerical model TOUGH2-LGM (Transport of Unsaturated Groundwater and Heat-Landfill Gas Migration) has been developed to simulate landfill gas production and migration processes within and beyond landfill boundaries. The model is derived from the general non-isothermal multiphase flow simulator TOUGH2, to which a new equation of state module is added. It simulates the migration of five components in partially saturated media: four fluid components (water, atmospheric air, methane and carbon dioxide) and one energy component (heat). The four fluid components are present in both the gas and liquid phases. The model incorporates gas-liquid partitioning of all fluid components by means of dissolution and volatilization. In addition to advection in the gas and liquid phase, multi-component diffusion is simulated in the gas phase. The landfill gas production rate is proportional to the organic substrate and is modeled as an exponentially decreasing function of time. The model is applied to the Montreal's CESM landfill site, which is located in a former limestone rock quarry. Existing data were used to characterize hydraulic properties of the waste and the limestone. Gas recovery data at the site were used to define the gas production model. Simulations in one and two dimensions are presented to investigate gas production and migration in the landfill, and in the surrounding limestone. The effects of a gas recovery well and landfill cover on gas migration are also discussed.