In this paper, a method for the determination of the relative and mass exhalation rates is presented. For the measurement of radon content in an emanation chamber, an a/b liquid scintillation counter was applied. The method was preliminarily tested on the following samples: (1) samples of uranium tailing piles in the Kowary region, (2) samples obtained by mixing of the mentioned waste with various materials such as cement, gypsum and anhydrite and (3) samples of some building materials.