A computational framework consisting of a one-way coupled hemodynamic-acoustic method and a wave-decomposition based post-processing approach is developed to investigate the biomechanics of arterial bruits. This framework is then applied to studying the effect of the shear wave on the generation and propagation of bruits from a modeled stenosed artery. The blood flow in the artery is solved by an immersed boundary method (IBM) based incompressible flow solver. The sound generation and propagation in the blood volume is modeled by the linearized perturbed compressible equations, while the sound propagation through the surrounding tissue is modeled by the linear elastic wave equation. A decomposition method is employed to separate the acoustic signal into a compression/longitudinal component (curl free) and a shear/transverse component (divergence free), and the sound signals from cases with and without the shear modulus are monitored on the epidermal surface and are analyzed to reveal the influence of the shear wave. The results show that the compression wave dominates the detected sound signal in the immediate vicinity of the stenosis whereas the shear wave has more influence on surface signals further downstream of the stenosis. The implications of these results on cardiac auscultation are discussed.