The final stages of creep rupture in a polycrystalline metal, by the linking-up of grain boundary microcracks to form a macroscopic crack, is studied by the numerical analysis of plane strain unit cells containing many hexagonal grains. Power law creep and elasticity are accounted for inside the grains, while intergranular failure occurs by cavity nucleation and growth to coalescence or by grain boundary sliding. The pattern of damage development initiated by an initial microcrack in the centre of the unit cell is studied for different stress states and different amounts of grain boundary viscosity. Furthermore, the model analyses are used to estimate the fraction of the total life time spent in the final link-up process. The life times are compared with estimates based on simple models that cannot describe microcrack linking-up.