An acoustic standing wave is used to trap and deform giant unilamellar vesicles with a diameter ranging from 10 to 50 μm. The giant unilamellar vesicles are prepared in glucose solution with a bi-layer of DOPC membrane with approximately 10 nm-thickness. They are suspended in a 4 cm2-chamber of an acoustofluidic device. The density of the vesicles is about 98% of the external solution density. The device operates with a single-frequency at 6 MHz producing a standing wave of 250 μm-wavelength, which is much larger than the vesicles' radii. To explain the observed deformability, we propose an acoustic deformation model as follows. The radiation stress, caused by the interaction of the standing wave and a vesicle, is obtained in the long-wavelength limit. Using the deformation theory of thin spherical shells, we show that the aspect ratio of a deformed vesicle is 1 + 2δ, where δ is inversely proportional to Young's modulus and directly proportional to the density contrast between the vesicle and the solution. Our preliminary observations and theoretical results give an aspect ratio of the same order of magnitude, δ<1/2. Additionally, predictions of our model agree with the results for the deformation of an osmotically swollen red blood cell reported by Mishra et al. [Biomicrofluidics 8, 034109 (2014)]. In this case, the relative error is smaller than 6%. [Work partially supported by Newton Advanced Fellowship (NA160200), The Royal Society, UK.]