The development of heat and moisture transport in concrete is critical to the development of pore pressures, which are thought to be a primary driver of damage and thermal spalling in concrete exposed to elevated temperatures. In the light of uncertainty and variation in the value of certain material properties and constitutive or parametric descriptions found in the literature, various sets of numerical experiments were conducted to investigate the significance of the intrinsic permeability, the evolution of permeability related to temperature and the relative permeability of the fluid phases as functions of saturation in predicting and analysing the behaviour of concrete drying under normal, low temperature, isothermal conditions and under exposure to very high temperature conditions as might be encountered during a fire. A fully coupled hygro-thermo-mechanical finite element model for concrete was employed with the permeability values and parametric functions altered in the model as required. Results of mass loss and the development of gas pressures with time were considered in relation to the potential for the occurrence of damage and thermal spalling, which is thought to be variously related to these processes. The analyses showed that permeability, and its variation with temperature, are very important in controlling the predicted behaviour at both low and high temperatures. Most significant of all were the relationships chosen to define the relative permeabilities. These were shown to strongly control the results of analyses of both low and high temperature problems and to potentially imply apparently different permeability values for the same concrete.