Bronchial asthma (BA) is a disease that still lacks an exhaustive treatment protocol. In this regard, the global medical community pays special attention to the genetic prerequisites for the occurrence of this disease. Therefore, the search for the genetic polymorphisms underlying bronchial asthma has expanded considerably. As the present study progressed, a significant amount of scientific medical literature was analyzed and 167 genes reported to be associated with the development of bronchial asthma were identified. A group of participants (n = 7,303) who had voluntarily provided their biomaterial (venous blood) to be used in the research conducted by the Federal Medical Biological Agency of Russia was formed to subsequently perform a bioinformatic verification of known associations and search for new ones. This group of participants was divided into four cohorts, including two sex-distinct cohorts of individuals with a history of asthma and two sex-distinct cohorts of apparently healthy individuals. A search for polymorphisms was made in each cohort among the selected genes, and genetic variants were identified whose difference in occurrence in the different cohorts was statistically significant (significance level less than 0.0001). The study revealed 11 polymorphisms that affect the development of asthma: four genetic variants (rs869106717, rs1461555098, rs189649077, and rs1199362453), which are more common in men with bronchial asthma compared to apparently healthy men; five genetic variants (rs1923038536, rs181066119, rs143247175, rs140597386, and rs762042586), which are more common in women with bronchial asthma compared to apparently healthy women; and two genetic variants (rs1219244986 and rs2291651) that are rare in women with a history of asthma.