We investigate the performance of the individual 2-D elastic full-waveform inversion (FWI) of Rayleigh and Love waves as well as the feasibility of a simultaneous joint FWI of both wave types. The FWI of surface waves can provide a valuable contribution to near-surface investigations, since they are mainly sensitive to the S-wave velocity and hold a high signal-to-noise ratio. In synthetic reconstruction tests we compare the performance of the individual wave type inversions and explore the benefits of a simultaneous joint inversion. In these tests both individual wave type inversions perform similarly well, given that the initial P-wave velocity model is accurate enough. In this case the joint FWI further improves the result. For an inaccurate initial P-wave velocity model, we observe artifacts in the results of the Rayleigh wave FWI and the joint FWI. Subsequently, we recorded a near-surface field dataset to verify the results by a realistic example. In the field data application the Love wave FWI is superior to the Rayleigh wave FWI, possibly due to the initial P-wave velocity model. Also in this case the joint FWI further improv ... mehres the inversion result.