This paper discusses the results of the analysis of the relationship between dose and solid cancer incidence among nuclear workers (males) who worked as liquidators after the Chernobyl accident. Information on this cohort of individuals is available at the regional center of Russian National Medical and Dosimetric Registry operating at the RF State Research Centre-Institute of Biophysics. Medical and dosimetric information on 8,654 persons 18-60 years of age with documented external radiation doses is used for the analysis. These data were gathered in the period from 1996 to 2001 and cover a total of 45,166.5 follow-up person-years. In the cohort under study, 179 solid cancers occurred during this period. The average age of liquidators at the time of exposure was 35.8 years, and the average dose as a result of the Chernobyl exposure was about 0.05 Sv. For an analysis of the dose-effect relationship (induction of radiation-induced malignant neoplasms) the statistical software EPICURE was used. The results of the analysis show that the cancer incidence in this cohort does not exceed cancer incidence in relevant age groups of the Russian population. The mean value of SIR for all cancer diseases was 0.88 (0.76, 1.02, 95% CI) for the whole period of follow-up. Risks for the induction of radiation-related cancer diseases were not statistically meaningful. Excess relative risk per 1 Sv was 0.95 (-1.52, 4.49, 95% CI).