The interaction between mangroves and storm surges is explored using an analytical solution. A simplified momentum equation, balancing vegetation drag and pressure gradient, is combined with the continuity equation resulting in a diffusion equation. Assuming a simplified environment, a one‐dimensional analytical solution is obtained to predict peak surge level across a forest. The solution accurately reproduces peak water level of a 10‐year return period flood event in mangroves in the Firth of Thames, New Zealand, and in Ten Thousand Islands, Florida, during Hurricane Charley. Vegetation properties that determine the capacity of mangroves to reduce surges are forest density and cross‐shore extent. Storm characteristics—flood duration and peak water level at the forest fringe—also influence surge attenuation. Mangroves are shown to be an effective form of coastal flood protection if forests are sufficiently wide/dense, relative to the surge decay length scale, to restrict water exchange during a storm. Plain Language Summary Storm‐driven flooding is a major hazard in low‐lying coastal areas. Mangroves have previously been shown to provide effective coastal protection from storm waves. However, there is sparse evidence that mangroves reduce storm surge, which is the temporary increase in water level resulting from the combination of high winds and low atmospheric pressure during a weather event. Here we demonstrate that mangroves can reduce water flow and store water, thus helping to reduce peak surge water levels. We show that if forests are sufficiently wide, water levels within (and landward of) the mangroves are substantially lower than for a scenario in which mangroves are absent. The density of the vegetation, cross‐shore extent of the forest, and characteristics of the surge (duration and amplitude) all influence water‐level reduction in the forest. Key Points An analytic solution is developed to describe storm surge propagation through coastal mangroves The water storage capacity of mangrove forests is shown to be as important as frictional effects in attenuating storm surge Reduction in peak storm surge level increases non‐linearly as mangrove forest width (cross‐shore) increases