The diffusion-accommodated sliding of irregularly shaped grain boundaries in two-dimensional bicrystals is considered. The following assumptions are made: the grains adjoining the boundaries are rigid, the boundaries do not support any shear stresses, sliding displacements are infinitesimal, and sliding is accommodated only by grain boundary diffusion. The solution to this problem is illustrated for a bicrystal with a grain boundary consisting of three segments. The results of calculations involving up to 35 segments agree with Raj and Ashby's theory for the sliding of periodic boundaries. The influence of boundary conditions on the normal stress distributions along grain boundaries is examined. Zero-flux conditions at the intersection of a grain boundary with a free surface, which correspond to low surface diffusivities, can lead to high normal grain boundary stresses. The stress distributions and sliding rates of boundaries containing randomly spaced equisized bumps or equispaced bumps of random size are compared to the periodic case (i.e., equispaced equisized bumps). Substantial normal stresses can build up at such nonperiodic grain boundaries.