Theoretical estimates or experimental determinations of stress fields associated with semiconductor devices are generally simplified with the aid of two elastic constants, Young's modulusEand Poisson's ratio &ngr;. In this paper, a generalized expression for &ngr; has been derived for arbitrary orientations of cubic semiconductor crystals, and the variation ofE, &ngr;, andE/(1‐&ngr;) for directions within the important {111}, {100}, and {110} planes is examined. The results show that isotropic elasticity theory is exact for all directions within {111} planes and that the composite elastic constantE/(1‐&ngr;) which frequently occurs in problems of practical interest is also invariant for all directions within {100} planes. Numerical values for the various elastic constants are tabulated for GaAs, GaP, Si, and Ge.