Karrenbach (1989) proposed a practical scheme to invert cross-well data for the case of a homogeneous, transversely isotropic medium, using the elliptic approximation and traveltime information for each component. I applied this homogeneous inversion scheme to a three-component cross-well dataset recorded by Western Geophysical. Unfortunately, it was not possible to detect a coherent SH arrival. Consequently, we were able to obtain only four elastic parameters from the estimated elliptic parameters. As an extension to the homogeneous inversion, I have derived a scheme for the more general case of a horizontally layered model and tested it in a synthetic dataset. In this scheme, the model is represented by a superposition of a basis set of symmetric and anti-symmetric square functions. When applied to the cross-well data, the layered inversion scheme generates a stable solution with associated traveltimes that show a better fit to the data than the homogeneous results. However, the insufficient amount of data used compromises the reliability of a higher resolution estimation. Nevertheless, the results obtained with the first few iterations (corresponding to the low frequency components of the model) can be still considered a reliable improvement in the resolution of the model.