This article describes an extension of the MARKAL energy model, in which the demands for energy services are elastic to their own prices. The new model is called MARKALED. In MARKALED, the user chooses a reference demand scenario, which is then used to calibrate a set of demand functions (one per demand segment) of arbitrary shape, but which, in this research, we assume to be with constant elasticity. The new model should prove useful in the context of analyzing scenarios where environmental taxes and/or constraints impose a significant strain on the various economic sectors, in the form of severe increases in the marginal costs of some energy services. The article also includes a series of demonstration runs of the MARKALED model for Ontario, and a brief analysis of the results, showing that the inclusion of elastic demands has a marked influence on the model response.