We present first results of applying a full-waveform inversion to synthetic and real upward-looking radar data underneath the snowpack at the Weissflujoch test site, Davos, Switzerland. The inversion is tested with a suite of selected scenarios of discrete reflection events from within the snowpack, with a focus on density and liquid water content. In a second step, the synthetic data mimic interferences of reflections events. Nevertheless, the full-waveform inversion is capable to converge to the synthetic model. A third step investigates the effect of white noise on the synthetic data. In the final step the inverse method is applied to a true data set. Despite some systematic differences, the inversion reproduces realistic changes in the physical properties, like density, of the snowpack.