High temperature structural materials must be resistant to cracking and oxidation. However, most oxidation resistant materials are brittle and a significant reduction in their yield stress is required if they are to be resistant to cracking. It is shown, using density functional theory, that if a crystal's unit cell elastically deforms in an inhomogeneous manner, the yield stress is greatly reduced, consistent with observations in layered compounds, such as Ti₃SiC₂, Nb₂Co₇, W₂B₅, Ta₂C and Ta₄C₃. The mechanism by which elastic inhomogeneity reduces the yield stress is explained and the effect demonstrated in a complex metallic alloy, even though the electronegativity differences within the unit cell are less than in the layered compounds. Substantial changes appear possible, suggesting this is a first step in developing a simple way of controlling plastic flow in non-metallic crystals, enabling materials with a greater oxidation resistance and hence a higher temperature capability to be used.