Cutaneous burn wounds represent a significant public health problem with 500,000 patients per year in the USA seeking medical attention. Immediately after skin burn injury, the volume of the wound burn expands due to a cascade of chemical reactions, including lipid peroxidation chain reactions. Such expansion threatens life and is therefore highly clinically significant. Based on these chemical reactions, the present paper develops for the first time a three-dimensional mathematical model to quantify the propagation of tissue damage within 12 hours post initial burn. We use the model to investigate the effect of supplemental antioxidant vitamin E for intercepting propagation. We show, for example, that if tissue levels of vitamin E tocotrienol are increased, postburn, by five times then this would slow down the lipid peroxide propagation by at least 50%. We chose the alpha-tocotrienol form of vitamin E as it is a potent inhibitor of 12-lipoxygenase, which is known to propagate oxidative lipid damage. Our model is formulated in terms of differential equations, and sensitivity analysis is performed on the parameters to ensure the robustness of the results.