This study describes the possibility for reducing the sonic boom by the use of non-axisymmetric body shapes, which are expected to more efficiently take advantage of the cut-off phenomenon of the atmosphere. If the propagation of high pressure shock waves can be restricted above the cut-off range, the sonic boom heard on the ground can be considerably alleviated. Therefore, a non-axisymmetric body shape was employed to create this asymmetric propagation of near-field pressure waves. In this paper, Triangle body, Diamond body, and four ideal bodies of revolution are studied and their initial boom intensities were compared. Near-field pressure and sonic boom signatures are examined quantitatively, using Computational Fluid Dynamics (CFD) in inviscid flow (Euler) mode and the Waveform Parameter Method. As for the results, the Triangle body in lift condition realized the asymmetric propagation and also the utilization of the cut-off phenomenon, thus alleviating the boom intensity on the ground as much as the 1/4th power body with a blunted-nose shape at no-lift condition.