Skeletal bone age assessment is a common clinical practice to diagnose endocrine and metabolic disorders in child development. In this paper, we describe a fully automated deep learning approach to the problem of bone age assessment using data from Pediatric Bone Age Challenge organized by RSNA 2017. The dataset for this competition is consisted of 12.6k radiological images of left hand labeled by the bone age and sex of patients. Our approach utilizes several deep learning architectures: U-Net, ResNet-50, and custom VGG-style neural networks trained end-to-end. We use images of whole hands as well as specific parts of a hand for both training and inference. This approach allows us to measure importance of specific hand bones for the automated bone age analysis. We further evaluate performance of the method in the context of skeletal development stages. Our approach outperforms other common methods for bone age assessment.