Elastic constants for zinc-blende and wurtzite AlN, GaN, and InN are obtained from density-functional-theory calculations utilizingab initiopseudopotentials and plane-wave expansions. Detailed comparisons are made with the available measured values and with results obtained in previous theoretical studies. These comparisons reveal clear discrepancies between the different sets of elastic constants which are further highlighted by examining derived quantities such as the perpendicular strain in a lattice-mismatched epitaxial film and the change in the wurtzitec/aratio under hydrostatic pressure. Trends among results for the three compounds are also examined as well as differences between results for the zinc-blende and wurtzite phases. ©1997 American Institute of Physics.