Recently Haastrup et al 2018 (2D Mater. 5 042002) introduced the Computational 2D Materials Database (C2DB), which organises a variety of structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 1500 two-dimensional materials distributed over more than 30 different crystal structures. Unfortunately, the work contains serious and fundamental flaws in the field of elasticity and mechanical stability tests that make it unreliable.