We are interested in reconstructing the normal velocity of a vibrating body using mea­sured values ofthe radiated pressure fi.eld. Firstly, some qualitative informations about the behaviour of this inverse problem are obtained through the examination of the particular case of the vibrating sphere, using its well-known analytical solution. Then, as we wish to deal with a vibrating body of arbitrary shape, we develop some algebraic features of the so-called Gaussian inversion method in order to stabilize the inversion and obtain confidence indicators on the result; in this case the direct problem is discretized using the boundary element method. Finally some numerical results are pre­sented in order to highlight the influence of several factors on the result: a priori informations, noisy experimental data, detection and elimination of erroneous data, if any.