Automatic forest stock volume (FSV) estimation is crucial for carbon and water cycle prediction, assessing climate change, forest resources management, and ecosystem analysis. In recent years, various researches focused on this problem utilizing high-resolution light detection and ranging (LiDAR) data. However, this type of data requires unmanned autonomous vehicles (UAVs) to be collected. In practical application, it leads to high data collection costs. This paper considers computer vision approaches that estimate FSV using only freely available satellite images (Sentinel-2 with 10 meters per pixel spatial resolution). Therefore, the satellite-based approach needs neither additional hardware nor human resources for data collection. It makes the method scalable and allows application in hard-to-reach regions. We implemented and compared the classical machine learning approaches and deep convolutional neural networks (CNNs) for the FSV estimation task. For model training and evaluation, field-based measurements from the Russian boreal forest were used with a total area of about 20000 hectares. The result shows the high potential of computer vision methods for robust forest resources assessment.