A model for temperature programmed desorption (TPD) of hydrogen from the Si(100)-2 x 1, Ge(100)-2 x 1, and SiGe alloy surfaces is presented. In the model, density functional theory is used to calculate the activation barriers of hydrogen desorption, and statistical mechanics is applied to determine the distribution of hydride species on the Si(100)-2 x 1, Ge(100)-2 x 1, and SiGe alloy surfaces using the DFT results. Hydrogen desorption via both the prepairing mechanism and the interdimer mechanisms is considered. The overall rates of hydrogen desorption from the surfaces are determined by the statistical model, and TPD spectra are simulated from the overall desorption rates. We find that, although the TPD spectra simulated according to the prepairing mechanism are consistent with the near-first-order kinetics observed experimentally on the Si(100)-2 x I and Ge(100)-2 x I surfaces, hydrogen desorption via interdimer mechanisms results in peak temperatures more consistent with experiments. We also consider two kinetic models which combine the contributions from both mechanisms and find better agreement with experiments in terms of both desorption peak temperatures and reaction orders. Finally, we have modeled hydrogen desorption from SiGe alloy surfaces.