Cable structures are a significant part of any long-span bridges as they account for the primary load-bearing members. Due to pitting corrosion and other breakages, the load-carrying capacity of bridge cables is affected and it is of paramount importance for the bridge engineers and stakeholders to monitor the existing infrastructures. Structural health monitoring (SHM) techniques are utilized to monitor such incidents and one of the prominent methods is to practice guided ultrasonic wave propagation and acoustic emission (AE) monitoring. In this paper, the numerical modeling of wave scattering by a structural discontinuity (cable damage) in axisymmetric high strength steel wire - viscoelastic waveguide medium for analyzing the wave interaction by inhomogeneity. This paper discusses the hybrid standard three-dimensional finite element (3D FE) method and semi-analytical finite element (SAFE) method for numerical analysis of guided ultrasonic wave propagation. The AE signal characteristics are used to understand the wave interaction of the pitting corrosion (damage) in steel wire cable considered for the present research work.