Herbicide resistance has become a major issue for many weeds. Metabolic resistance refers to the biochemical processes within organisms that degrade herbicides to less toxic compounds, resulting in a shift of the dose response curve. This type of resistance involves polygenic inheritance. A model is presented linking the biochemical pathway of amino acid synthesis and the detoxifying pathway of an inhibitor of the key enzyme ALS. From this model, resistance factors for each biotype are derived, which are then applied to a polygenic population genetic model for an annual weed plant. Polygenic inheritance is described by a new approach based on tensor products of heredity matrices. Important results from the model are that low dose regimes favour fast emergence of resistant biotypes and that the emergence of resistant biotypes occurs as abrupt outbreaks. The model is used to evaluate strategies for the management of metabolic resistance.