The Young’s modulus, E, and Poisson’s ratio, nu, can be used for theoretical calculation or experimental determination of residual stresses arising during the growth of wide band gap semiconductor thin films. In this paper, a generalized expression for nu and El(1-nu) for the hexagonal closed packed (hcp) structure common to wide band gap semiconductors has been given for the first time. In addition, the specific expressions for E, nu, and El(1-nu) are given for directions within the c and r planes in the hcp structure. These elastic constants are found to be invariant within the c plane but not within the r plane. Numerical values for these elastic constants are computed and listed for 6H-SiC, Al2O3, and AlN.