Natural control methods based on surface electromyography (sEMG) and pattern recognition are promising for hand prosthetics. However, the control robustness offered by scientific research is still not sufficient for many real life applications, and commercial prostheses are capable of offering natural control for only a few movements. In recent years deep learning revolutionized several fields of machine learning, including computer vision and speech recognition. Our objective is to test its methods for natural control of robotic hands via sEMG using a large number of intact subjects and amputees. We tested convolutional networks for the classification of an average of 50 hand movements in 67 intact subjects and 11 transradial amputees. The simple architecture of the neural network allowed to make several tests in order to evaluate the effect of pre-processing, layer architecture, data augmentation and optimization. The classification results are compared with a set of classical classification methods applied on the same datasets. The classification accuracy obtained with convolutional neural networks using the proposed architecture is higher than the average results obtained with the classical classification methods, but lower than the results obtained with the best reference methods in our tests. The results show that convolutional neural networks with a very simple architecture can produce accurate results comparable to the average classical classification methods. They show that several factors (including pre-processing, the architecture of the net and the optimization parameters) can be fundamental for the analysis of sEMG data. Larger networks can achieve higher accuracy on computer vision and object recognition tasks. This fact suggests that it may be interesting to evaluate if larger networks can increase sEMG classification accuracy too.