Full-waveform inversion (FWI) has been implemented mostly for isotropic media, with extensions to anisotropic models typically limited to acoustic approximations. Here, we develop elastic FWI for transmitted waves in 2D heterogeneous VTI (transversely isotropic with a vertical symmetry axis) media. The model is parameterized in terms of the P- and S-wave vertical velocities and the P-wave normal-moveout and horizontal velocities. To test the FWI algorithm, we introduce Gaussian anomalies in the Thomsen parameters of a homogeneous VTI medium and perform FWI of transmission data for different configurations of the source and receiver arrays. The inversion results strongly depend on the acquisition geometry and the aperture because of the parameter trade-offs. In contrast to acoustic FWI, the elastic inversion helps constrain the S-wave vertical velocity, which for our model is decoupled from the other parameters.