Despite the intense development of deep neural networks for computer vision, and especially semantic segmentation, their application to Earth Observation data remains usually below accuracy requirements brought by real-life scenarios. Even if well-known deep learning methods produce excellent results, they tend to be over-confident and cannot assess how relevant their predictions are. In this work, a Bayesian deep learning method, based on Monte Carlo Dropout, is proposed to tackle semantic segmentation of aerial and satellite images. Bayesian deep learning can provide both a semantic segmentation and uncertainty maps. Based on the popular U-Net architecture, our model achieves semantic segmentation with high accuracy, e.g. F1-score and overall accuracy respectively reaching 90.84% and 93.22% on a public standard dataset. Uncertainty maps, also derived from our model, show a strong interest in qualitative evaluation of the segmentation and in the improvement of the database.