The generation of shock waves and their repercussions in high-speed vehicles are inevitable. Particularly, the hot plume from the aircraft exhaust ejecting at a high speed, as well as the emitted aeroacoustic noise, have several consequences. Besides, the occurrence of the supersonic core length and the emission of high screech noise are mostly due to the shock cells, prevailing in high-speed jets. Therefore, understanding the shock cell structures developed at the exit of aircraft or rocket nozzles is vital in improving mixing and thereby the noise characteristics. Essentially, non-Circular nozzle shapes are well known for enhancing entrainment characteristics and mitigating the noise due to their differential spreading over the nozzle's perimeter. The current study examines the shock structures of Circular, elliptic, and square jets at various sonic underexpansion levels. In this investigation, the nozzle geometries are considered to have the same exit area. The Nozzle Pressure Ratio (NPR) was adjusted to 3, 4, and 5 to achieve moderate and highly underexpansion conditions. The shadowgraph visualization method is used to study the development of shock cells from axisymmetric and asymmetric nozzles. It is interesting to observe that the incident and reflected shock structures exist only at moderate and high underexpansion levels. Besides, the elliptic and the square jets have distinctive flow patterns along their different axis planes. The intercepting shock appears on the elliptic jet in the minor axis rather than the major axis direction. The curvature of the intercepting shock wave was found to be greater for the elliptic jet than that for the Circular jet. In addition, the square jet in the symmetry plane diverges from the jet centerline, but the jet in the diagonal direction converges. Moreover, the estimated shock cell lengths using shadowgraph images were compared to a theoretical model where the experimentally obtained results are in good agreement with the theoretical values.