Previous work using in-situ curvature measurement has shown a correlation between stress and microstructure during the early stages of thin film growth. The model presented here can be used to predict the curvature change of the substrate during part of this growth process. Curvature, and thus film stress, is measured in-situ during growth of sputter-deposited Pt on amorphous substrates. The average film stress is observed to be slightly compressive initially, followed by a change towards a tensile maximum, after which the stress becomes compressive again. Plan view TEM micrographs of Pt films of thicknesses up to 35 Å show the evolution of microstructure from isolated islands to a coalesced film. This evidence suggests that the tensile regime is due to island coalescence. The model calculates the curvature induced in a substrate during the tensile excursion associated with island coalescence, where discontinuous islands are modeled as a series of cracks in an otherwise continuous film. Quantitative measurements of island size and areal fraction covered are extracted from the TEM micrographs and used to predict the curvature during coalescence. The predicted stresses are shown to compare favorably with the measured stresses.