This thesis describes algorithms developed to jointly estimate vocal tract shapes and source signals from real speech. The methodology was developed and evaluated using simple articulatory models of the vocal tract, coupled with lumped parametric models of the loss mechanisms in the tract. The vocal tract is modelled by a five parameter area function model [Lm, 1990] Energy losses due to wall vibration and glottal resistance are modelled as a pole- zero filter placed at the glottis. A model described in [Lame, 1982] is used to approximate the lip radiation characteristic. An articulatory-to-acoustic "linked codebook" of approximately 1600 shapes is generated and exhaustively searched to estimate the vocal tract parameters. Glottal waveforms (input signals) are obtained by inverse filtering real speech using the estimated vocal tract parameters. The inverse filter is constructed using the estimated area function. A new method is proposed to fit the Liljencrants - Fant glottal flow model [Fant, Liljencrants and Lm, 1985] to the inverse filtered signals Estimates of the parameters are found from both the inverse filtered signal and its derivative. The descnbed model successfully estimates articulatory parameters for artificial speech waveforms. Tests on recorded vowels suggest that the technique is applicable to real speech. The technique has applications in the development of natural sounding speech synthesis, the treatment of speech disorders and the reduction of data bit rates in speech coding