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The topic of this contribution is the mechanical modeling of solution-precipitation creep, a process occurring in polycrystalline and granular structures under specific temperature and pressure conditions. The model presented has a variational structure and is based on a novel proposal for the dissipation while the elastic energy is kept in the standard form. The assumed dissipation term depends on two kinds of velocities characteristic for the process: velocity of material transfer and velocity of inelastic deformations, both manifesting themselves on the boundaries of the grains. For the numerical implementation, the standard finite element program FEAP together with the pre- and postprocessing software package GID are used. The simulations are illustrated by two examples, a polycrystal with regular hexagonal microstructure and a polycrystal with random microstructure.