The long-term behaviour, particularly shrinkage and creep, of concrete exposed to environments in which the relative humidity is low and the temperature is high is uncertain. Most existing creep and shrinkage models impose limits on relative humidity such that they cannot be used when the relative humidity is low. This thesis investigates the ability of creep and shrinkage models, despite the imposed limit on relative humidity, to predict both the overall behaviour of concrete specimens exposed to extreme conditions and the internal behaviour of thick concrete sections exposed to extreme conditions which differ on either side. Results suggest that the limit on relative humidity may be ignored and that model predictions conservatively estimate long-term structural behaviour.