Dense anisotropic carbons are praised materials for thermostructural applications, yet, so far, a detailed structure-property relationship for these materials is still lacking, especially for the pyrocarbon (pyC) matrices in carbon/carbon composites. Here we compute the full elastic tensors of 210 recently introduced nanoscale models of anisotropic carbons [Polewczyk et al. Carbon 212 (2023) 118109], covering domain sizes (L$_c$ and L$_a$ ) and orientation angles (OA, as a measure of nanotexture) relevant to most as-prepared and moderately heat-treated pyC matrices: L c ∈ [1.5:8 nm]; L a ∈ [2:5.5 nm]; and OA ∈ [25:110 • ]. Isothermal and adiabatic elastic tensors, corresponding to the slow quasi-static and ultra-fast loading regimes, respectively, are considered. Analysing the database of computed elastic constants with a random forest regressor supervised learning algorithm we show that all elastic constants can be predicted accurately using L$_c$ , L a and OA as descriptors. Among the latter, OA is the one showing, by far, the strongest correlation with the elastic tensors. For such dense, non porous carbons, 3 of the 6 isothermal and 5 of the 6 adiabatic constants can even be accurately predicted using OA as the unique material descriptor. Calculation of the universal anisotropy index shows that isothermal tensors show more anisotropy than adiabatic ones, indicating that stress relaxation favors elastic anisotropy. Eventually, the Young's moduli and Poisson coefficients of six models of actual pyCs are presented and their longitudinal moduli compared to tensile measurements, showing relatively poor agreement. These results suggest that accounting for texture at a larger scale is required to capture pyC matrices elasticity.