We propose to combine recent Convolutional Neural Networks (CNN) models with depth imaging to obtain a reliable and fast multi-person pose estimation algorithm applicable to Human Robot Interaction (HRI) scenarios. Our hypothesis is that depth images contain less structures and are easier to process than RGB images while keeping the required information for human detection and pose inference, thus allowing the use of simpler networks for the task. Our contributions are threefold. (i) we propose a fast and efficient network based on residual blocks (called RPM) for body landmark localization from depth images; (ii) we created a public dataset DIH comprising more than 170k synthetic images of human bodies with various shapes and viewpoints as well as real (annotated) data for evaluation; (iii) we show that our model trained on synthetic data from scratch can perform well on real data, obtaining similar results to larger models initialized with pre-trained networks. It thus provides a good trade-off between performance and computation. Experiments on real data demonstrate the validity of our approach.