Damage to fasteners during hydroturbine units operation may lead to serious consequences and in special cases to technological disasters. Technical condition of most critical fastening elements is determined based on non-destructive testing. However, this approach does not exclude the possibility of sudden damage to fastening elements, which affects safety and reliability of hydroturbine equipment operation. Monitoring the stress–strain state of fastening elements helps prevent sudden damage. However, most methods of stress–strain state assessment have significant limitations when used in complicated industrial operating conditions. The article presents the experience of using the metal magnetic memory (MMM) method for monitoring the stress–strain state of studs for cover attachment to the hydraulic turbine stator. Based on self-magnetic stray fields’ distribution analysis, the article demonstrates that the actual studs stress–strain state may differ significantly from the estimated one. At the same time, inspection using the MMM method detected stress concentration zones (SCZs), which are the source of local plastic strain and subsequent damage development in the course of operation. Comprehensive material studies in SCZs confirmed critical changes in the mechanical characteristics, which confirmed the efficiency of the MMM method application.