Strain-stiffening-an increase in material stiffness at large strains-is a vital mechanism by which many soft biological materials thwart excessive deformation to protect tissue integrity(1-3). Understanding the fundamental science of strain-stiffening and incorporating this concept into the design of metals and ceramics for advanced applications is an attractive prospect. Using cementite (Fe3C) and aluminium borocarbide (Al3BC3) as prototypes, here we show via quantum-mechanical calculations that strain-stiffening also occurs, surprisingly, in simple inorganic crystalline solids and confers exceptionally high strengths to these two solids, which have anomalously low resistance to deformation near equilibrium. For Fe3C and Al3BC3, their ideal shear strength to shear modulus ratios attain remarkably high values of 1.14 and 1.34 along the (010)[ 001] and (0001) [01 (1) over bar0] slip systems, respectively. These values are more than seven times larger than the original Frenkel value of 1/2 pi (refs 4, 5) and are the highest yet reported for crystalline solids. The extraordinary stiffening of Fe3C arises from the strain-induced reversible 'cross-linking' between weakly coupled edge- and corner-sharing Fe6C slabs. This new bond formation creates a strong, three-dimensional covalent bond network that resists large shear deformation. Unlike Fe3C, no new bond forms in Al3BC3 but stiffening still occurs because strong repulsion between Al and B in a compressed Al-B bond unsettles the existing covalent bond network. These discoveries challenge the conventional wisdom that large shear modulus is a reliable predictor of hardness and strength of materials(4-7), and provide new lessons for materials selection and design.