High harmonic generation (HHG) from solid has opened up exciting opportunities in both fundamental physics and potential applications. It provides a unique platform for the study of strong-field and ultrafast electron dynamics in the condensed phase. Two-dimensional materials exhibit remarkable electronic properties with wide tunability, and strain engineering is an important way to tune the properties of such materials. However, control of HHG by strain engineering of materials has remained largely unexplored. Here we report controllable HHG by tuning the electronic structures via mechanical engineering. Using first-principles calculations, we show that the HHG process is sensitive to strains, which leads to a significant enhancement of harmonic intensity.