Measurements of piezoelectric coefficients d33 and d31 in wurtzite GaN and AlN using an interferometric technique are presented. We report on the clamped values, d33c of these coefficients found in GaN and AlN thin films, and we derive the respective bulk values, d33b. The clamped value of d33c in GaN single crystal films is 2.8±0.1 pm V-1 which is 30% higher than in polycrystalline films grown by laser assisted chemical vapor deposition. The value of d33b in bulk single crystal GaN is found to be 3.7±0.1 pm V-1. The value of d33c in plasma assisted and laser assisted chemical vapor deposited AlN films was 3.2±0.3 and 4.0±0.1 pm V-1, respectively. The bulk value estimate of d33b in AlN of 5.6±0.2 pm V-1 was deduced. The values of d31, both clamped and bulk, were calculated for wurtzite GaN and AlN. We have also calculated the values of d14 in cubic phase film and bulk GaN and AlN. Interferometric measurements of the inverse piezoelectric effect provide a simple method of identifying the positive direction of the c axis, which was found to be pointing away from the substrate for all films.