The vocal tract (VT) of a singer acts as a filter on the acoustic output from the vibrating vocal folds, enhancing several frequency bands whose peaks are called formants. The nature of these formants is characterized by the shape and dimensions of the VT and they are numbered with the first formant being the lowest in frequency. Perceptually, the first (F1) and second (F2) formants indicate the vowel being sung while the third (F3), fourth (F4) and fifth (F5) relate to the timbre or tone color of the output sound. It is therefore relevant to the understanding of the vocal organ to be able to measure the resonances of the tract with precision. Here we apply the exponential sine sweep method used in room acoustics to VT models and replicas. We use an exponential sine sweep as the source signal for the cavity and record its output. After convolving the output signal with the appropriate inverse filter, we can separate the linear impulse response of the tract from its harmonic distortions. This method is both applied on VT models of Chiba and Kajiyama and on MRI-based molded VTs.