The extent to which metal particle geometry and adsorbate spillover influence the temperature-programmed desorption spectra for the desorption of hydrogen from supported-metal catalysts has been studied by Monte Carlo simulation. By including a mechanism for adsorbate spillover and surface diffusion it is shown that spillover of the adsorbate onto the catalyst support can result in the differences observed experimentally between desorption spectra obtained from single crystals and supported-metal catalysts. An isosteric Arrhenius analysis of the TPD spectra has been used to demonstrate that, at low surface coverage, the activation energy characterising surface diffusion of adsorbates on the catalyst support can be obtained from the desorption spectrum.