The adverse effects of flood events have been increasing in the world due to the increasing occurrence frequency and their severity due to urbanization and the population growth. All weather sensors, such as satellite synthetic aperture radars (SAR) enable the extent detection and magnitude analysis of such events under cloudy atmospheric conditions. Sentinel-1 satellite from European Space Agency (ESA) facilitate such studies thanks to the free distribution, the regular data acquisition scheme and the availability of open source software. However, various difficulties in the visual interpretation and processing exist due to the size and the nature of the SAR data. The supervised machine learning algorithms have increasingly been used for automatic flood extent mapping. However, the use of Convolutional Neural Networks (CNNs) for this purpose is relatively new and requires further investigations. In this study, the U-Net architecture for multi-class segmentation of flooded areas and flooded vegetation was employed by using Sentinel-1 SAR data and altitude information as input. The training data was produced by an automatic thresholding approach using OTSU method in Sardoba, Uzbekistan and Sagaing, Myanmar. The results were validated in Ordu, Turkey and in Ca River, Vietnam by visual comparison with previously produced flood maps. The results show that CNNs have great potential in classifying flooded areas and flooded vegetation even when trained in areas with different geographical setting. The F1 scores obtained in the study for flood and flooded vegetation classes were 0.91 and 0.85, respectively.