We study the influence of the growth kinetics on the Asaro-Tiller-Grinfel'd instability of a thin film deposited on a patterned substrate. We use a continuum model that we solve at first order in the surface slope. Both wetting interactions and elastic fields induced by the film/substrate interface introduce an explicit dependence on the film thickness. As a consequence, the translational symmetry in the growth direction is broken and the deposition flux cannot be trivially accounted for. Similarly to the evolution during annealing, the instability can skip during growth from an in-phase to an out-of-phase geometry depending on the growth duration and film thickness. We compare the evolution of the instability using different deposition fluxes. We find that the kinetic phase diagram found in the annealing case also explains the evolution during growth in usual growth conditions. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.