Based on the transformed stiffness constants for ultra-thin layers of hexagonal crystals, we have derived explicitly the Hookian relation and the strain energy density for the stressed overlayers (10 (1) over bar0), (11 (2) over bar0), (10 (1) over bar1) and (11 (2) over bar2). Calculations have been partly carried out by a computer programme. Several important applications of the strain energy density related to dislocations, kink, monatomic step and stacking faults are discussed. Many opto-electronic devices based on hexagonal compounds such as 6H-SiC, ZnO and GaN exhibit the above phenomena as well as misfit dislocations, stresses and strains. Appropriate experimental techniques for the strain energy density measurements are suggested.