Multiple sclerosis (MS) is regarded as multifactorial, polygenic disease; its development is the result of autoimmune and neurodegenerative processes which lead to multifocal lesions of the central nervous system. The aim of the study was to analyze associations between MS and polymorphic markers rs3129934 (C6orf10), rs1109670 (DDEF2/MBOAT2 gene), rs9523762 (GPC5 gene), rs28362491 (NFKB1 gene), rs10974944 (JAK2 gene), and rs2304256 (TYK2 gene). The material for the study was DNA samples of unrelated MS patients (N = 224) aged 17 to 67 years and individuals of a control group (N = 312) aged 18 to 66 years. Both samples were formed from the ethnic group of Russians. The results of the investigation demonstrated that, for women, MS was associated with genotypes rs3129934*C/T (p = 0.001, OR = 2.23), rs3129934*T/T (p = 0.028, OR = 4.04), and rs2304256*C/C (p = 0.049, OR = 1.6); for men, with genotype rs1109670*C/A (p = 0.017, OR = 2.06). In addition, using the APSampler algorithm, we identified combinations of alleles associated with increased risk of MS separately for women and men, in which the most frequent alleles of polymorphic markers were rs3129934*T, rs1109670*C, rs10974944*G, and rs2304256*C.