Several techniques can be used to reconstruct the internal geometry of a wind instrument from acoustics measurements. In this study, the passive linear acoustic response of the instrument is simulated and an optimization process is used to fit the simulation to the measurements. This technique can be seen as a first step toward the design of wind instruments, where the targeted acoustics properties come no more longer from measurements but are imposed by the designer. The difficulties of this approach are to find the best acoustic observation allowing the reconstruction (impedance, reflection function, etc.) but also to have an efficient optimization process. The "full waveform in-version" (FWI) is a technique coming from the seismol-ogy community. It uses the knowledge of the equation modeling the wave propagation into the instrument (here the telegraphist equation) to have an explicit expression of the gradient of the function which is minimized. This gradient is evaluated with a low computational cost. The FWI methodology, along with 1D spectral finite element discretization in space, applied to the woodwind instruments (with tone holes, losses and radiation) is presented in this communication. The results obtained for the bore reconstruction with different acoustics observations are then compared and discussed.