miRNAs regulate gene expression by binding with mRNAs of many genes. Studying their effects on genes involved in oncogenesis is important in cancer diagnostics and therapeutics. The RNAHybrid 2.1 program was used to predict the strong miRNA binding sites (p < 0.0005) in target mRNAs. The program Finder 2.2 was created to verify 784 intergenic miRNAs (ig-miRNA) origin. Among 54 considered oncogenes and tumor suppressor genes, 47 genes are the best targets for ig-miRNAs. Accordingly, these genes are strongly regulated by 111 ig-miRNAs. Some miRNAs bind several mRNAs, and some mRNAs have several binding sites for miRNAs. Of the 54 mRNAs, 21.8%, 43.0%, and 35.2% of the miRNA binding sites are present in the 5'UTRs, CDSes, and 3'UTRs, respectively. The average density of the binding sites for miRNAs in the 5'UTR was 4.4 times and 4.1 times greater than in the CDS and the 3'UTR, respectively. Three types of interactions between miRNAs and mRNAs were identified, which differ according to the region of the miRNA bound to the mRNA: 1) binding occurs predominantly via the 3'-region of the miRNA; 2) binding occurs predominantly through the central region of the miRNA; and 3) binding occurs predominantly via the 5'-region of the miRNA. Several miRNAs effectively regulate only one gene, and this information could be useful in molecular medicine to modulate translation of the target mRNA. We recommend described new sites for validation by experimental investigation.