This thesis reports on the application of ground penetrating radar (GPR) as a non-destructive technique for the monitoring of ring separation in brick masonry arch bridges. In addition, research is reported on the assessment of the clay capping layer often used in construction as a waterproof backing to arches. The thrust of the research is numerical modelling, verified by large laboratory experiments. Due to the heterogeneity of these structures, the resultant signals from the interaction between the GPR system and the bridge are often complex and hence, hard to interpret. This highlighted the need to create a GPR numerical model that would allow the study of the attributes of reflected signals from various targets within the structure of the bridge. The GPR numerical analysis was undertaken using the finite-difference time-domain (FDTD) method. Since micro regions in the bridge structure need to be modelled, the introduction of subgrids of supporting finer spatial resolution into the standard FDTD method was considered essential in order to economise on the required computational resources. In the main part of this thesis, it is demonstrated how realistic numerical modelling of GPR using the FDTD method could greatly benefit from the implementation of subgrids into the conventional FDTD mesh. This is particularly important when (a) parts of the computational domain need to be modelled in detail (i.e., ring separation between the mortar layers and the brick units, which is the case studied in this thesis); and also (b) when there are features or regions in the overall computational mesh with values of high relative permittivity supporting propagation of waves at very short wavelengths. A scheme is presented that simplifies the process of implementing these subgrids into the traditional FDTD method. This scheme is based on the combination of the standard FDTD method and the unconditionally stable alternating-direction implicit (ADI) FDTD technique. Given that ADI-FDTD is unconditionally stable, its time-step can be set to any value that facilitates the accurate calculation of the electromagnetic fields. By doing so, the two grids can efficiently communicate information across their boundary without requiring to use a time-interpolation scheme. The performance of ADI-FDTD subgrids when implemented into the traditional FDTD method is discussed herein. The developed algorithm can handle cases where the subgrid crosses dielectrically inhomogeneous and/or conductive media. In addition, results from the comparison between the proposed scheme and a commonly employed purely FDTD subgridding technique are presented. After determination of the optimum ADI-FDTD scheme, numerical experiments were conducted and calibrated using GPR laboratory experiments. Good correlations were obtained between the numerical experiments and the actual GPR experiments. It was shown both numerically and experimentally that significant mortar loss between the masonry arch rings can be detected. Dry hairline delaminations between the mortar and the brick masonry are difficult to detect using standard GPR procedures. However, hairline faults containing water produce distinct and detectable GPR responses. In addition, the clay layer was successfully identified and its thickness calculated to a satisfactory accuracy.