The molecular modeling method is promising for the assessment of protein structure, being able to present an energetically beneficial protein conformation with atomic precision. This method is of great importance for studying molecular interactions and confirming pathogenic significance of the changes in the protein structure caused by particular mutations. In the present study we used molecular modeling for the assessment of mutations in the SOD1 gene in patients with amyotrophic lateral sclerosis (ALS), a severe neurodegenerative disorder characterized by the loss of the spinal and cerebral motor neurons. The product of SOD1 is a cytosolic dimeric enzyme Cu/Zn superoxide dismutase (SOD1) responsible for detoxification of the cellular superoxide radicals. We showed that all 8 revealed coding point mutations of the gene led to moderate or significant changes of the SOD1 protein energy. Mutation His49Arg increased the protein energy, and reconstruction of the respective model pointed out to spatial destabilization of the molecule and abnormal interaction with the metal ion inside the active center. The other 7 mutations (Gly17Ala, Leu85Mal, Asn87Ser, Asp91Ala, Serl06Leu, Glu134Gly, and Leul45Phe), on the contrary, led to decrease of the protein energy and increase of the spatial stability of SOD1, which is usually accompanied by increased propensity of the 'inert' mutant molecule to misfolding and cellular aggregation. Thereby, the results of in silico analysis of the SOD1 gene mutations confirm staying of ALS within the class of the so-called conformational diseases of the central nervous system, a characteristic feature of which is forming of cytotoxic insoluble protein inclusions in neurons.