This work highlights the effect of pressure ranging from 0 to 9 GPa on structural, directional dependent mechanical properties and unravel the previously unknown phase transitions of two important high energy molecular solids namely monoclinic-β-Nitrotriazole (NTO) and 2,4,6-triamino-1,3,5-trinitrobenzene (TATB). The projected augmented plane wave method with generalized gradient approximation Perdew–Burke–Ernzerhof functional with the D2 van der Waals corrections method of Grimme is used to reproduce the experimental data within ∼1% error. The structural optimization results reveal that β-NTO undergoes a previously unknown structural phase transition at 9 GPa which is evident from the abrupt change of calculated lattice vectors, volume (V), lattice angle β at 9 GPa. The single crystal elastic properties analysis also supports these findings and NTO voilate the Born’s mechanical stability criteria at 9 GPa. Besides to it, all the calculated volumetric and directional dependent shear modulus (G), bulk modulus (B), compressibility results of β-NTO in (100), (010), (001) planes also suggest a possible phase transition around 9 GPa. The directional dependent polycrystalline compressibility anisotropy analysis of TATB with pressure in (100), (010), (001) planes unreveal the origin of experimentally reported new phase transition around 4 GPa. The calculated Pugh B/G ratio suggests that, both the materials found to be brittle in the studied pressure range except NTO at 9 GPa. The degree of mechanical anisotropy of β-NTO found to increase with increasing pressure from (100)–(010)–(001) planes, while the TATB anisotropy results were found to be relatively small and stable. The Young’s modulus (E), Poisson’s ratio (σ), P-wave modulus, universal elastic anisotropy (A ), Chung-Buessen anisotropy (A ), Vickers hardness coefficient (H ), sound velocities ((V ) average, (V ) longitudinal, (V ) transverse) and (θ D ) Debye temperature are also predicted. The calculated intermolecular interaction strength contribution to the total Hirsh Field Surface at different pressures confirms the initial decomposition mechanism of NTO, TATB and the results are good in agreement with previous observations. Thus our work has accentuated the reasons behind the impact and friction sensitivity differences of β-NTO, TATB through the two new phase transitions.