A low-dimensional physical model of small-amplitude oscillations of the vocal folds is proposed here. The model is a simplified version of the body-cover one in which mucosal surface wave propagation has been approximated by the seesaw-like oscillation of the vocal fold about its fulcrum point whose position is adjustable in both the horizontal and vertical directions. This approach works for 180 degree phase difference between the glottal entry and exit displacements. The fulcrum point position has a significant role in determining the shape of the glottal flow. The vertical position of the fulcrum point determines the amplitude of the glottal exit displacement, while its horizontal position governs the shape and amplitude of the glottal flow. An increment in its horizontal position leads to an increase in the amplitude of the glottal flow and the time period of the opening and closing phases, as well as a decrease in the time period of the closed phase. The proposed model is validated by comparing its results with the low-dimensional mucosal surface wave propagation model.