Tensile stresses that arise during the growth of polycrystalline films are described using a cohesive zone approach, along with a finite element model that accounts for different dihedral angles at grain boundary intersections with the growth surface. This combined approach predicts the maximum tensile stress as a function of the grain size and the grain boundary/surface energies. These relationships differ from those proposed previously. The model also indicates that grain boundary cusps can have a significant effect on the magnitude of tensile growth stresses, with sharper grain boundary cusps leading to lower steady-state tensile stresses in the film. Data from several materials with large tensile growth stresses are in reasonable agreement with the model. In particular, AlN films grown by metal organic chemical vapor deposition exhibit tensile stresses that are at or near the maximum predicted tensile values. The experimental results from these nitride films are also consistent with two other model predictions for growth at the tensile limit: the stresses are (i) independent of the growth rate and (ii) at (or close to) the fracture limit.