A practical possibility of specific alpha-activity measurement of the radioactive waste (RAW) as much as thousands tons placed in the 4-th Chornobyl wrecking unit is demonstrated by means of determination of the helium content (on the account of Pu, Am decay) in the hermetic containers filled with the RAW. The method using application of helium filter is acceptable but filterless one seems to be more economical. The latter is based on a constraint of all gases into choused gaseous medium but helium. The appraisal of necessary time for passive helium accumulation up to partial pressure of ~10⁻⁷ Pa (a value to be measured by mass-spectrometer) is of ~1000 hours using a scheme with real helium filter and of ~10 hours in the case without filter for specific alpha-activity of ~10⁵ Bq/kg. (a threshold level for the RAW disposition).