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A mesoscopic discrete dislocation dynamics is presented which is used to study constrained diffusional creep in polycrystalline thin films. Recent experimental work has shown that ultrathin polycrystalline films on substrates reveal a transition in the deformation behavior. Continuum modeling and atomistic simulation were used successfully to explain this transition as a shift from plastic deformation by dislocation slip on inclined slip planes for larger film thicknesses to diffusional creep for the smallest film thicknesses. During the creep process material from the surface migrates into the grain boundaries. Due to the constraint of the substrate, this diffusional creep builds up large internal stresses that are responsible for dislocation glide on slip planes parallel to the film surface on which there is no resolved shear stress in the overall equibiaxial stress field. This process is investigated quantitatively with a discrete dislocation model describing diffusional creep as climb of dislocations and taking into account the slip on parallel slip planes relaxing the internal stresses. The results are shown to be consistent with experiment under certain assumptions, and thus help to identify the critical deformation processes during creep of ultrathin films.