Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim of the present work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularisation is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov regularisation and parameter-choice methods not requiring an error norm estimate for choosing the right amount of regularisation. We demonstrate that the L-curve criterion is robust with respect to the errors in real measurement situations.