The earliest forms of cellular life would have required a membrane compartment capable of growth and division. Fatty acid vesicles are an attractive model of protocell membranes, as they can grow into filamentous vesicles that readily divide while retaining their contents. In order to study vesicle growth, we have developed a method for immobilizing multilamellar fatty acid vesicles on modified glass surfaces and inducing filamentous membrane growth under flow. Filament formation strictly depended on the presence of freshly neutralized fatty acid micelles in the flow chamber. Using light microscopy, we observed a strong dependence of initial growth velocity on initial vesicle size, suggesting that new fatty acid molecules were incorporated into the membrane over the entire external surface of the vesicle. We examined the influences of flow rate, fatty acid concentration, and salt concentration on filamentous growth and observed drastic shape changes, including membrane pearling, of preexisting membrane tubules in response to osmotic stress. These results illustrate the versatility of flow studies for exploring the process of fatty acid vesicle growth following exposure to free fatty acids.