The elastic and mechanical properties of organic molecular crystals of active pharmaceutical ingredients (API) are crucial for their development into solid dosage forms. A drug substance with poor mechanical properties can have instability and formulation issues. Experimentally determining mechanical properties of molecular crystals can be time-consuming and often offer limited information. However, the maturity of dispersion-inclusive density-functional theory (DFT) over recent years has enabled the predictive investigation of stability and properties of molecular crystals. Furthermore, the development of faster DFT based methods such as density functional tightbinding (DFTB) has, when appropriately benchmarked, enabled economical alternatives for the study of large molecular crystals. Here, a benchmark study of DFT and DFTB is performed by determining the elastic constants of a series of archetypal crystal structures and APIs, including polymorphic forms of paracetamol and aspirin, urea and benzene. In addition, the structure-mechanics relations of the considered systems are established. DFT semi-quantitatively predicts elastic properties but shows excellent qualitative agreement when compared to experiment. Similarly, DFTB yields an excellent qualitative agreement with experiment. This demonstrates the possibility of DFTB to be employed as a DFT surrogate. Lastly, it is found that the direction of the largest resistance of the Young’s modulus coincides with key structural features, such as hydrogen bonding and π − π interactions. The established protocols for the determination of elastic properties open up the possibility of characterizing the elastic and mechanical properties of crystal structures that exhibit novel mechanical behaviour and even of those of postulated solid forms from crystal structure prediction studies.