The isomer shift calibration constants have been calculated for 57.60 keV in I-127 and for 27.72 keV in I-129 resonant transitions by density functional theory. The full-potential linearized augmented plane-wave method (FLAPW) was applied in the scalar-relativistic approach. The NaI compound was used to set the origin of the scales in both cases. On the basis of the existing experimental data, the following values for the calibration constants were obtained: alpha =- 0.057(2) mm s(-1) au(3) for I-127 and alpha = +0.164(4) mm s(-1) au(3) for I-129. The ratio of the calibration constants of alpha(127)/alpha(129) =- 0.35(1) was established. Spectroscopic electric quadrupole moments for the ground state of the above nuclei have been calculated as byproduct. The quadrupole moments Q(g)((127)) = -0.764(30) b and Q(g)((129)) = -0.731(3) b were obtained for I-127 and I-129, respectively. Errors quoted are due to the linear regression fit, and real errors might be as large as about 10% of the quoted absolute value.