We present the results from the X-ray spectral analysis of high-redshift active galactic nuclei (AGN) in the Chandra Deep Field South (CDFS), making use of the new 4 Ms data set and new X-ray spectral models from Brightman & Nandra, which account for Compton scattering and the geometry of the circumnuclear material. Our goals are to ascertain to what extent the torus paradigm of local AGN is applicable at earlier epochs and to evaluate the evolution of the Compton thick fraction with redshift, important for X-ray background synthesis models and understanding the accretion history of the Universe. In addition to the torus models, we measure the fraction of scattered nuclear light, fscatt, known to be dependent on the covering factor of the circumnuclear material, and use this to aid in our understanding of its geometry. We find that the covering factor of the circumnuclear material is correlated with the line-of-sight column density NH, and as such the most heavily obscured AGN are in fact also the most geometrically buried. We come to these conclusions from the result that fscatt decreases as NH increases and from the prevalence of the torus model with the smallest opening angle as the best-fitting model in the fits to the most obscured AGN. We find that a significant fraction of sources (∼20 per cent) in the CDFS are likely to be buried in material with close to 4π coverage having been best fitted by the torus model with a 0° opening angle. Furthermore, we find 41 Compton thick sources in the CDFS using the new torus models, 29 of which we report here for the first time. We bin our sample by redshift in order to investigate the evolution of the Compton thick fraction by epoch. We take into account the incompleteness and contamination rates in the spectral identification of Compton thick AGN using data from simulations. We also account for the bias against the X-ray selection of heavily obscured sources due to flux suppression in the Chandra band, by restricting to intrinsic luminosities at which the CDFS is sensitive to Compton thick AGN (LX∼ 1044 at z= 2.5). We find a significant increase in the intrinsic Compton thick fraction, normalized to LX= 1043.5 erg s−1, from ≈20 per cent in the local Universe to ≈40 per cent at z=1 - 4.