This study deals with the ill-posed problem of inversion of the articulatory-to-acoustic relationship, i.e. the recovery of vocal tract geometry from formant frequencies. A small database of articulatory-acoustic data has been established for one subject. A midsagittal-to-area function conversion model, which works both for vowels and fricative consonants, has been developed from these data. This model has finally been used as a major constraint for an optimisation algorithm based on a gradient descent technique, in order to regularise the solution and solve the inversion problem. Other spatial and temporal smoothing constraints have been also used. Single configurations, as well as entire [VC] sequences could be recovered, using adequate initial conditions.