This short communication presents a flow perturbation model for filament buckling that is typically observed under smectic A liquid crystal phase ordering from the isotropic phase. In the absence of flow, liquid crystal filaments buckle with a characteristic wave-length under the action of negative tension generated by the decrease in free energy that drives the growth process. This phenomenon is demonstrated numerically using simulations of a previously presented non-driven mesoscopic model. We then investigate how shear and extensional flow affect the filament buckling process. Using a linearized model, the filament shape dynamics are cast into a Cahn-Hilliard equation whose solutions are the buckling modes. The growth rate of the dominant mode is expressed in terms of the factorized product of the elastic contribution and the flow contribution. The flow Deborah number, D-e, contributions to the growth of the dominant wave-vector are found to be root 1 +/- n D-e, where + (-) denotes compression (extension), and where n = 2 (1/2) for planar extensional (shear) flow. The model provides insights on how flow-generated stresses affect shape formation, an area of significant interest to biological form and growth. (c) 2008 Elsevier B.V. All rights reserved.