Some experimental data concerning stress effect on grain boundary (GB) diffusion and models describing the GB diffusion (GBD) in thin polycrystalline films for the B- and C-regimes under a stress field are reviewed. Numerical solutions for the conditions of reflecting free surface and rapid surface diffusion on the sink surface for the case of a constant source are obtained. The results of the model calculations are compared with the results of the investigation of Cu GBD in Ni thin films and with experimental data from the literature. The comparative influence of the GBD atomic mechanisms on the shape of GBD penetration plots is discussed.