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Accurate and timely mapping of flood extent from high-resolution satellite imagery plays a crucial role in disaster management such as damage assessment and relief activities. However, current state-of-the-art solutions are based on U-Net, which cannot segment the flood pixels accurately due to the ambiguous pixels (e.g., tree canopies, clouds) that prevent a direct judgement from only the spectral features. Thanks to the digital elevation model (DEM) data readily available from sources such as United States Geological Survey (USGS), this work explores the use of an elevation map to improve flood extent mapping. We propose, EvaNet, an elevation-guided segmentation model based on the encoder-decoder architecture with two novel techniques: (1) a loss function encoding the physical law of gravity that if a location is flooded (resp. dry), then its adjacent locations with a lower (resp. higher) elevation must also be flooded (resp. dry); (2) a new (de)convolution operation that integrates the elevation map by a location-sensitive gating mechanism to regulate how much spectral features flow through adjacent layers. Extensive experiments show that EvaNet significantly outperforms the U-Net baselines, and works as a perfect drop-in replacement for U-Net in existing solutions to flood extent mapping. EvaNet is open-sourced at https://github.com/MTSami/EvaNet