The paper analyses the VSP data inversion in order to determine elastic constants of a transversely isotropic medium with a horizontal axis of symmetry of an infinite order (HTI), simulating an oriented fractured reservoir. Acquisition system of VSP is characterized by the absence of sub-horizontal directions of propagation of seismic waves. In this regard, it was necessary to determine the accuracy with which the elastic constants of the anisotropic layer are restored. The seismograms of the full wave field were selected as the initial data, calculated synthetically for the model of the medium containing azimuthally anisotropic layers. A complex of compressional and shear waves propagating from a source and recorded in the well. In such layers, the shear wave incident on the roof of the HTI layer splits into two waves that propagate at different velocities and have a mutually orthogonal displacement vectors. The processing task was to select waves S1 and S2 and build their arrival time curves. These arrival time curves were used in the inversion. The inversion was solved in the form of minimizing the functional of the mean square residual. Elastic constants, determined by inversion, almost exactly coincided with the model ones. The results obtained show the validity of the chosen approach for solving the inverse problem.