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Elemental balance, the property of having the same number of each type of atom on both sides of the equation, is a fundamental feature of chemical reactions. In metabolic network models, this property is typically verified on a reaction-by-reaction basis. In this paper we show how violations of elemental balance can be efficiently detected in an entire network, without the need for specifying the chemical formula of each of the metabolites, which enhances a modeler's ability to automatically verify that their model satisfies elemental balance. Our method makes use of duality theory, linear programming, and mixed integer linear programming, and runs efficiently on genome-scale metabolic networks (GSMNs). We detect elemental balance violations in 40 out of 84 metabolic network models in the BiGG database. We also identify a short list of reactions that are candidates for being elementally imbalanced. Out of these candidates, nearly half turn out to be truly imbalanced reactions, and the rest can be seen as witnesses of elemental balance violations elsewhere in the network. The majority of these violations involve a proton imbalance, a known challenge of metabolic network reconstruction. Our approach is efficient, easy to use and powerful. It can be helpful to metabolic network modelers during model verification. Our methods are fully integrated into the MONGOOSE software suite and are available at https://github.com/WGS-TB/MongooseGUI3.