Computer simulation experiments and numerical modelling studies have been used to recover the P-wave anisotropic elastic parameters for transversely isotropic media with a tilted symmetry axis (TTI media). These parameters include P-wave velocity along the axis of symmetry α0, S-wave velocity along the axis of symmetry s0, the P-wave anisotropy e, and the near-vertical P-wave anisotropy d. The angle of tilt in such media also has been recovered. The Levenberg-Marquardt method is utilised in carrying out the iterative inversion to recover the elastic parameters and angle of tilt ?using a set of transmission data. This paper presents the 2-D case in which the vertical plane through the survey line contains the anisotropic axis of symmetry. The method was tested numerically on single layer models created with published anisotropic parameters having a range of tilt angles from zero to 90°. Traveltimes were computed using in-house software based on computed ray velocity (group velocity) functions. The traveltime data were inverted to recover the elastic parameters and the tilt angles of the symmetry axis. Results obtained are in good agreement with model parameters. In order to evaluate the performance of the inversion scheme in practice, random noise was added to the model data. The inversion algorithm proved to be robust and good results were obtained in the presence of noise. VSP field data were also successfully processed using the inversion program. The software includes options of constraining parameters to improve inversion accuracy. Elastic parameter recovery from field data may be used to improve the accuracy of pre-stack depth migration, depth estimation and reservoir volume estimations. Currently, VSP data must be recorded with dip direction for inversion with this 2-D software. Extension to the general 3-D case is currently being planned.