In order to recover the movements of usually hidden articulators such as tongue or velum, we have developed a data-based speech inversion method. HMMs are trained, in a multistream framework, from two synchronous streams: articulatory movements measured by EMA, and MFCC + energy from the speech signal. A speech recognition procedure based on the acoustic part of the HMMs delivers the chain of phonemes and together with their durations, information that is subsequently used by a trajectory formation procedure based on the articulatory part of the HMMs to synthesise the articulatory movements. The RMS reconstruction error ranged between 1.1 and 2. mm.