The elastic strain limit, which quantifies the elastic flexibility of a material, is critical for technological applications of functional materials in a number of fields. Although the elastic flexibility of molecular crystals has been recognized, the extent of elastic flexibility of such materials remains to be defined. Here, we report a molecular crystal, i.e., form I polymorph of celecoxib (CEL), exhibiting exceptional elastic flexibility with an elastic strain of at least 8.70%. The record high elastic strain is accompanied by low Young’s modulus (E = 3.18 ± 1.01 GPa) and hardness (H = 39.8 ± 15.6 MPa), as determined by single crystal nanoindentation, along with the high plasticity of the bulk powder observed in in-die Heckel analysis.