The vibration of the vocal folds produces the primary sound source for vowels. This paper first reviews vocal fold anatomy and the kinematics associated with typical vibratory motion. A brief historical background is then presented on the basic physics of vocal fold vibration and various efforts directed at mathematical modeling of the vocal folds. Finally, a low-dimensional model is used to simulate the vocal fold vibration under various conditions of vocal tract loading. In particular, a “no-tract” case is compared to two cases in which the voice source is coupled to vocal tract area functions representing the vowels /i/ and /a/, respectively.