This paper suggests a theoretical explanation of bag and bag-with-a-stamen formation. The analysis treats hydrodynamic instability due to inertial forces of drop acceleration as a mechanism of breakup at low Weber numbers, and elaborates a model of deformed drop, regarded as an accelerating liquid layer, for instability treatment. The linear inviscid instability analysis shows that the development of aperiodic unstable disturbances can be the real mechanism for generating bag and bag-with-a-stamen formation, which is preliminary to drop disintegration. The critical Weber numbers for the different breakup regimes are obtained theoretically. The results of the investigation provide a simple theoretical explanation of complicated modes of breakup such as "bag" and "claviform." Some reasons for causing a "chaotic" type breakup are also suggested.