This paper presents the results of a feasibility cytogenetic study using the fluorescence in situ hybridization (FISH) translocation assay for residents of villages located on the Techa River (Southern Urals, Russia) contaminated with liquid radioactive wastes from the Mayak plutonium facility in 1949–1956. The study was conducted with two groups of donors that differed in their main pathways of exposure. The first group comprised 18 residents of the middle Techa region who were exposed predominantly from ingestion of radionuclides (mostly ^89,90Sr) via the river water and local foodstuffs. The second group included 20 residents of Metlino, the closest village to the site of releases, who were exposed to external γ radiation from the contaminated river bank and exposed internally from dietary intake of radionuclides. A significant linear dependence between the radiation-induced translocation frequency and individual red bone marrow dose from incorporated ^89,90Sr, calculated with the Techa River Dosimetry System (TRDS), was found in the first group of donors. This allowed us to take the contribution of ^89,90Sr to the total radiation-induced translocation frequency into account for the second group of donors and to analyze translocations resulting from external γ-ray exposure. Individual doses from external exposure derived from the corrected translocation frequency for the second group of donors (Metlino residents), using a linear dose–response coefficient of 0.015 translocation/cell/Gy recommended by Edwards et al. in 2005, were shown to vary up to 2.1 Gy, with an average value of 0.48 Gy, which was in agreement with TRDS-based external dose estimates for Metlino residents.