Accurate spatial information of agricultural fields is important for providing actionable information to farmers, managers, and policymakers. On the other hand, the automated detection of field boundaries is a challenging task due to their small size, irregular shape and the use of mixed-cropping systems making field boundaries vaguely defined. In this paper, we propose a strategy for field boundary detection based on the fully convolutional network architecture called ResU-Net. The benefits of this model are two-fold: first, residual units ease training of deep networks. Second, rich skip connections within the network could facilitate information propagation, allowing us to design networks with fewer parameters but better performance in comparison with the traditional U-Net model. An extensive experimental analysis is performed over the whole of Denmark using Sentinel-2 images and comparing several U-Net and ResU-Net field boundary detection algorithms. The presented results show that the ResU-Net model has a better performance with an average F1 score of 0.90 and average Jaccard coefficient of 0.80 in comparison to the U-Net model with an average F1 score of 0.88 and an average Jaccard coefficient of 0.77.