A novel, but by now, well tried and tested approach to the mathematical modelling of the extraction life-cycle of any depleting fossil-fuel resource has been developed. It is a bottom-up technique for energy planning, whereby an integrated summation of the outputs from the various producing fields in the considered region is obtained. As the present paper will show, in the absence of political interference, this means for predicting the resulting future availabilities of the mineral fuels has been validated. Even in the event of a fiscal change, the model can be adjusted to take account of the new scenario. The evolved 'skewed-normal profile for the rate of-extraction' supply model (i) yields a better representation than has been achieved with earlier approaches and (ii) is appropriate for use with rate-of-extraction data. that rise with time to a plateau, and then decline more slowly, but is unsatisfactory for use when the profile exhibits more than a single rate-of-extraction peak. Also, in many circumstances, the profile is less systematic in shape, often as a result of temporary political, economic or on-stream changes. Thus, for these situations, it is proposed that a 'skewed-normal profile extraction' supply model be used in conjunction with what is here described as the reverse-projection technique. The application of the model, without and with reverse projections for the UK crude-oil and natural-gas extraction-rates data, is demonstrated. Reasonable predictions, for both crude-oil and natural-gas rates of demand, can be achieved only for a country that is politically and economically stable. Even then, because of uncertainties and social factors, it is often difficult to formulate a wise policy concerning long-term fuel requirements. Nevertheless, it is only by understanding the implications of changing fuel-demands that a long-term strategy can be evolved for a country's economy. Thus, it is desirable to try to predict the future requirements for crude oil and natural gas, and so, as an additional tool, a 'modified logit-function' demand model has been developed for use with the usually readily-available historic consumption data. It is based on extrapolations, using reasonable-trend assumptions, for the appropriate energy-intensity (i.e. annual fuel consumptionl/annual gross domestic product (GDP)), population and GDP/capita likely future behaviours.