Voice disorders are common physiological challenges that arise largely due to vocal fatigue, i.e. fatigue of vocal folds and associated phonatory structures. Since the incurrence of fatigue in vocal folds directly depends on the qualitative and quantitative nature of the dynamical signature of vocal fold oscillations, the hitherto literature has resorted to estimating the time histories and stress histories of the vocal fold oscillations. Often, vocal fold dynamics are rid with different types of complexities. Therefore, the literature often resorts to the use of a mathematical model that closely resembles the human phonatory system. Modelling the mechanism of vocal folds as a two-mass model with 2DOF provides a reasonably accurate depiction of the same. In order to obtain the real-time histories of the vocal fold vibrations, a continuously changing parameter called phonation threshold pressure (PTP) is defined so as to describe the extent of accumulated fatigue. PTP can be determined numerically for a given set of physical and physiological parameters of the system. Since the vocal fold vibrations are of varying amplitude as time progresses, it is necessary to use a standard counting algorithm for fatigue analysis, like the Rainflow-Counting algorithm. Then, the incurred damage is computed with the help of a S-N curve and the Miner’s rule. With the time span of phonation as the control parameter and PTP as a continuously changing parameter, the responses of the system are systematically obtained. Later, comparisons on the fatigue damage are made. © 2021, Springer Nature Singapore Pte Ltd.