Motivation: The concept of Elementary Flux Mode (EFM) has been widely used for the past 20 years. However, its application to genomescale metabolic networks (GSMNs) is still under development because of methodological limitations. Therefore, novel approaches are demanded to extend the application of EFMs. A novel family of methods based on optimization is emerging that provides us with a subset of EFMs. Because the calculation of the whole set of EFMs goes beyond our capacity, performing a selective search is a proper strategy. Results: Here, we present a novel mathematical approach calculating EFMs fulfilling additional linear constraints. We validated our approach based on two metabolic networks in which all the EFMs can be obtained. Finally, we analyzed the performance of our methodology in the GSMN of the yeast Saccharomyces cerevisiae by calculating EFMs producing ethanol with a given minimum carbon yield. Overall, this new approach opens new avenues for the calculation of EFMs in GSMNs.