This paper theoretically investigates the dynamics of internal drop motion and presents significant conclusions with respect to the role of deformational flow in drop fragmentation at low Weber numbers. The influence of deformational flow results in a selection mechanism between "bag," "claviform," and "multimode" breakup modes. This paper and conclusions are based on both the formulated instability necessary conditions and an advanced mathematical model of an accelerating and deforming drop. The analysis takes into account the pressure and surface tension force distributions along an ellipsoidal drop surface as well as the increasing gas velocity at a drop equator, caused by the flattening. It is suggested that the gas velocity values along an ellipsoid surface are the same as for a sphere at points where the angles between the normal vector to drop surface and the stream direction are the same. The numerical solutions of derived equations are used in analyzing the mass force field formation inside an accelerating and deforming drop and two stages of this process are established. It is shown that the distortion of the inertial force field, caused by deformation, causes the selection between breakup modes This paper concludes that during the first stage the deformational flow prevails over the drop's aerodynamic entrainment. Thus, the transiency and nonuniformity of the inertial force field, which are caused by the deformation, prevent "bag" early formation and result in either a "claviform" or a "multimode" mode at the later stage.