Finite element method based numerical simulations are performed to identify low-velocity impact-induced asymmetrically-located delamination in the$[0/90_3]_S$ and $[0/90]_{2S}$ composite plates, respectively, using a fundamental symmetric guided wave mode ($S_0$). The wave attenuation effect due to the viscoelasticity of the composite material is modeled by calculating the Lamb wave attenuation constants and using the Rayleigh proportional damping model. The estimated sizes and locations of the delamination in both plates were in good agreement with the experimental measurements. Moreover, the analysis of wave structure of the impacted plates shows that when the $S_0$ mode propagates through the damaged region, the delamination mouth opens up due to the presence of standing waves, which are generated as a consequence of multiple reflections of trapped waves with the delamination boundaries.