Partitioning of fatty acids into phospholipid membranes is studied on giant unilamellar vesicles (GUVs) utilizing phase-contrast microscopy. With use of a micropipet, an individual GUV is transferred from a vesicle suspension in a mixed glucose/sucrose solution into an isomolar glycerol solution with a small amount of oleic acid added. Oleic acid molecules intercalate into the phospholipid membrane and thus increase the membrane area, while glycerol permeates into the vesicle interior and thus via osmotic inflation causes an increase of the vesicle volume. The conditions are chosen at which a vesicle swells as a sphere. At sufficiently low oleic acid concentrations, when the critical membrane strain is reached, the membrane bursts and part of vesicle content is ejected, upon which the membrane reseals and the swelling commences again. The radius of the vesicle before and after the burst is determined at different concentrations of oleic acid in suspension. The results of our experiments show that the oleic acid partitioning increases when the membrane strain is increased. The observed behavior is interpreted on the basis of a tension-dependent intercalation of oleic acid into the membrane.