The half-lives of Sr90 and Cs137 were measured by the method of observing the disintegration rate rate of a known number of atoms. A 4(pi) proportional counter was designed and constructed to measure the absolute disintegration rates of the samples used. The efficiency of the counter was tested with calibrated radioactive solutions from the National Bureau of Standards. The submicrogram quantities of the carrier-free radioisotopes used for counting were determined with the mass spectrometer along with isotope dilution techniques. Independent evidence is given to support the half-lives found in this investigation. / Thesis / Master of Science (MS)