This paper investigates the gradient aspect of flapping in American English, considering both the language internal factors stress and morphological complexity and the language external factor lexical frequency. To reflect the gradient aspect of flapping, flapping rates were regarded as dependent variables, and a statistical analysis was conducted with both language-internal and language-external factors. Due to the range of dependent variables [0, 1], a zero/one inflated beta regression was conducted. The results verified that the more frequent a carrier word containing a word-medial /t/ is, the more likely it is for the word-medial /t/ to be realized as a flap, and that the wordmedial /t/ in a morphologically simple word is more likely to be realized as a flap than one in a morphologically complex word. Thereafter, Noisy Harmonic Grammar analyses were performed, and the extended version showed an improvement over the original model of 83.228%. (Hankuk University of Foreign Studies)