Polarization-maintaining fiber Bragg gratings (PM-FBGs) are a type of fiber optic sensor that is designed to maintain the polarization of light propagating through it. Polarization-maintaining single-mode fibers (PM fibers) use stress elements integrated into the fiber cladding to break the fiber symmetry. This allows light to be guided in two perpendicular principle states of polarization (with different propagation constants), known as the fast and slow axes. PM-FBG sensor has the potential to be used for mode separation because it possesses selective sensitivity to the S0 and A0 modes of the lamb waves. PM-FBG sensors principle and application is relatively new in structural health monitoring (SHM). Their behaviour is complex and difficult to predict without accurate numerical modelling. Therefore this paper aims to develop a validated numerical model for the PM-FBG sensor. A transverse strain based transfer matrix implementation is carried out to visualize the PM-FBG spectrum and simulate the guided wave (GW) sensing phenomena in the PM-FBG. The numerical model makes use of non-matching meshes through the use of interface elements. This allows different meshing on the structure and the optical fiber, which helps reduce the computational load. Furthermore, spectral element method is used for the modelling which has been known to outperform the conventional finite element modelling techniques. In addition, the simulated numerical model is then used to calculate the PM-FBG response using the transfer matrix implementation at the PM-FBG specifically. This validated numerical model provides a valuable tool for improving our knowledge of PM-FBG sensors and optimizing their design for SHM applications.