Droplet atomization through aerobreakup is omnipresent in various natural and industrial processes. Atomization of Newtonian droplets is a well-studied area; however, non-Newtonian droplets have received less attention despite their frequent encounters. By subjecting polymeric droplets of different concentration to the induced airflow behind a moving shock wave, we explore the role of elasticity in modulating the aerobreakup of viscoelastic droplets. Three distinct modes of aerobreakup are identified for a wide range of Weber number (∼ 10 2 − 10 4 ) and Elasticity number (∼ 10 −4 − 10 2 ) variation; these modes are-vibrational, shear-induced entrainment and catastrophic breakup mode. Each mode is described as a three stage process. Stage-I is the droplet deformation, stage-II is the appearance and growth of hydrodynamic instabilities, and stage-III is the evolution of liquid mass morphology. It is observed that elasticity plays an insignificant role in the first two stages, but a dominant role in the final stage. The results are described with the support of adequate mathematical analysis.