Micropipette aspiration technique can be very useful for describing the shape transitions of lipid bilayer vesicles with fluid phase coexistence modulated by the line tension and the bending rigidity. For example, composition dependence of the line tension at the liquid-ordered and liquid-disordered phase interface has been investigated using this technique. Recently, using a very simple mechanical model, the instabilities that occur during suction and release experiments of aspirated vesicles have been discussed. Due to its simplicity the model could not predict the influence of the bending rigidity. In this work, we incorporate the contributions from Helfrich bending energy and the line energy in the vesicle free energy and investigate the shape transitions in micropipette aspirated vesicles. We discuss how the critical aspiration pressure depends on the bending moduli of the phases, the line tension at the interface, and the reduced volume of the vesicle. The ratio of the bending moduli that we predict using the critical aspiration pressure data from recent experiments agrees with the literature. © 2010 The American Physical Society.