The research of fractographic images of metals is an important method that allows obtaining valuable information about the physical and mechanical properties of a metallic specimen, determining the causes of its fracture, and developing models for optimizing its properties. One of the main lines of research in this case is studying the characteristics of the dimples of viscous detachment, which are formed on the metal surface in the process of its fracture. This paper proposes a method for detecting dimples of viscous detachment on a fractographic image, which is based on using a convolutional neural network. Compared to classical image processing algorithms, the use of the neural network significantly reduces the number of parameters to be adjusted manually. In addition, when being trained, the neural network can reveal a lot more characteristic features that affect the quality of recognition in a positive way. This makes the method more versatile and accurate. We investigated 17 models of convolutional neural networks with different structures and selected the optimal variant in terms of accuracy and speed. The proposed neural network classifies image pixels into two categories: “dimple” and “edge”. A transition from a probabilistic result at the output of the neural network to an unambiguously clear classification is proposed. The results obtained using the neural network were compared to the results obtained using a previously developed algorithm based on a set of filters. It has been found that the results are very similar (more than 90% similarity), but the neural network reveals the necessary features more accurately than the previous method.