Recently Bar-Ziv and Moses discovered a dramatic, dynamical shape transformation induced in cylindrical lipid bilayer vesicles by the action of laser tweezers. We develop a hydrodynamic theory of fluid bilayers in interaction with the surrounding water to explain their video micrographs. Applying the marginal stability criterion to this situation gives us predictions for the selected initial wavelength and the propagation velocity, both in agreement with the experimental values. In particular we show that the instability initially propagates as a front at constant velocity, as observed. Finally we introduce an approximate hydrodynamic model applicable to the fully nonlinear regime. This model exhibits propagating fronts as well as fully-developed ``pearled" vesicles similar to those seen in the experiments.