Non-destructive evaluation plays a pivotal role in ensuring the safety and longevity of civil infrastructures. The application of shear horizontal (SH) waves significantly enhanced the field of NDE, primarily due to their unique characteristic of maintaining a consistent mode of propagation without converting into other wave modes when encountering interfaces or defects within the material. This offers a substantial advantage over other wave-based non-destructive evaluation techniques due to its stable non-mode converted signals, simplifying the interpretation of inspection results. In this study, the development of a spectral element method-based model for simulating SH wave propagation in cement-mortar medium has been discussed. Spectral element simulations are performed on a block, considering the mortar properties. The recorded signals from sensor positions in the simulated model are recorded and analyzed to detect boundaries and interfaces between different media. The result from the numerical model is validated with the experimental results, and comparable agreement is observed in terms of the time of flight of the wave packets. The developed model results are also compared with the finite element method-based model, and the results show significant agreement. The developed modeling technique can be used to investigate the SH wave propagation in homogeneous and heterogeneous media.