The growth stress generated once grains coalesce in Volmer-Weber-type thin films is investigated by time-multiscale simulations comprising complementary modules of (i) finite-element modeling to address the interactions between grains happening at atomic vibration time scales ($ 0:1 ps), (ii) dynamic scaling to account for the surface stress relaxation via morphology changes at surface diffusion time scales ($ s-ms), and (iii) the mesoscopic rate equation approach to simulate the bulk stress relaxation at deposition time scales ($ sec-h). On the basis of addressing the main experimental evidence reported so far on the topic dealt with, the simulation results provide key findings concerning the interplay between anisotropic grain interactions at complementary space scales, deposition conditions (such as flux and mobility), and mechanisms of stress accommodation-relaxation, which underlies the origin, nature and spatial distribution, and the flux dependence of the postcoalescence growth stress.