This study demonstrates the effect of a substrate layer of adipose tissue on the modal response of the vocal folds, and hence, on the mechanics of voice production. Modal analysis is performed on the vocal fold structure with a lateral layer of adipose tissue. A finite element model is employed, and the first six mode shapes and modal frequencies are studied. The results show significant changes in modal frequencies and substantial variation in mode shapes depending on the strain rate of the adipose tissue. These findings highlight the importance of considering adipose tissue in computational vocal fold modeling.