A theoretical study of the vibrational spectrum of the CS2 molecule is carried out. For that purpose, a new Morse-cosine potential energy function is determined by fitting to observed vibrational frequencies, using as a starting point an ab initio force field. Highly excited vibrational states for CS2 are then calculated up to 20 000 cm(-1) using a DVR truncation-diagonalization method. Hyperspherical Radau coordinates, which are a set of normal curvilinear coordinates for linear symmetric triatomic molecules, are used in these calculations. The computed vibrational energy levels are shown to present an excellent agreement with the observed values up to 13 000 cm(-1). Based on these calculations, some unassigned observed vibrational frequencies are identified and the assignments of others are reconsidered. Inspection is made of the vibrational wave functions computed for CS2 revealing a persistent regularity up to 13 000 cm(-1). This regularity is found to be consistent with perturbation theory results for these energies. Van Vleck perturbation theory is used to derive effective Hamiltonians that contain polyad quantum numbers and that provide good agreement with the variational calculations. It is also shown that the asymmetric stretch is practically decoupled from the symmetric stretch and the bend in this range of energies. The nearest neighbor space distribution (NNSD) and the Delta(3) spectral rigidity function show that the calculated vibrational spectrum of CS2 up to 20 000 cm(-1) is essentially regular, in agreement with the most recent statistical analyses made of the spectroscopically observed frequencies.