A method for measuring the activity of high-intensity radioactive sources via registration of innerbremsstrahlung spectra was developed. Equations that connect the spectrum shape to the activity of different parts of a source and to the γ activity of background impurities were obtained. A technique was developed that allows unambiguous elimination of the detector influence on spectral measurements. A procedure for modeling the passage of γ radiation through the source substance and protection is described, and the calculation of the germanium-detector response functions, which was performed with the Monte Carlo method using the Geant4 package, is presented. The developed method can be used for independent measurements of the activity of neutrino sources of the 51 Cr and 37 Ar type as an alternative to calorimetric measurements.