In order for the increased use of fiber-reinforced composite structures to be financially feasible, employment of reliable and economical systems to detect damage and evaluate structural integrity is necessary. This task has traditionally been performed using off-line non-destructive testing (NDT) techniques. Safety enhancement programs and cost minimization schemes for repairs, however, have substantially increased the demand for real time integrity monitoring systems, i.e. structural health monitoring (SHM) systems, in the past few years. The real time feature imposes an additional constraint on SHM systems to be fast and computationally efficient. Among the existing approaches fulfilling these requirements, guided ultrasonic wave (GUW)-based methods are of particular interest, since they provide the possibility of finding small size defects, both at the surface and internal, and covering relatively large areas with reasonable hardware costs. Next to theses appealing features, there are certain complexities in utilizing GUWs for SHM of fiber-reinforced composites, that mainly arise from the multi-layer, anisotropic, and non-homogeneous nature of the material. In addition, the multi-mode character of GUWs further increases the complexity of the SHM problem in these materials. It is believed that computationally efficient methods for simulation of GUWs in composite structures can substantially contribute to the field of SHM. Such numerical tools do not only improve the understanding of the propagation of ultrasonic waves and their interaction with different damage types and boundary conditions, but can also make model-based damage identification techniques feasible in the context of on-line SHM. In this dissertation an improved framework for simulation of GUWs in composite structures is developed. The improvements are mainly brought about through the use of (i) physical constraints that reduces the dimensionality of the problem, (ii) improved approximation bases for spatial and temporal discretization of the governing equations, and (iii) efficient mathematical tools to enable the possibility of parallel computation. The formulated approach is a wavelet-based spectral finite element method (WSFEM), which offers the possibility of complete decoupling of the spatial and temporal discretization schemes, and results in parallel implementation of the temporal solution. Although the concept of the WSFEM was introduced a few years prior to this research, to the author's best knowledge, no general framework was proposed for dealing with 2D and 3D problems with inhomogeneity, anisotropy, geometrical complexity, and arbitrary boundary conditions. These issues are addressed in this dissertation in multiple steps as described below. 1- Improvement of the temporal discretization using compactly-supported wavelets, by computing the operators of the wavelet-Galerkin method over finite intervals, and demonstrating about 50% reduction in the number of sampling points, with the same accuracy, compared to the conventional wavelet-based approach. 2- Extension of the existing formulation of the 1D WSFEM based on an in-plane displacement field to 1D waveguides based on a 3D displacement field. In the 1D finite element formulation, spectral shape functions are employed which satisfy the governing equations, in which shear deformation and thickness contraction effects are also incorporated. The minimum number of elements for modeling 1D waveguides is used in this approach. 3- Formulation of a novel 2D WSFEM in which frequency-dependent basis functions are suggested for spatial discretization. Contrary to the conventional WSFEM, the presented scheme discretizes the spatial domain with 2D elements and does not require extra treatments for non-periodic boundary conditions. Superior properties of the formulation are shown in comparison with some time domain FEM schemes. 4- Generalization of the WSFEM and extension to 3D geometries. It is demonstrated that the standard spatial discretization schemes can be combined with the wavelet-Galerkin approach, to fully parallelize the temporal solution. A higher-order pseudo-spectral finite element method, i.e. spectral element method (SEM), is further adopted to attain spectral convergence properties over space and time. The developed WSFEM is subsequently employed in the passive time reversal (TR) method, which is a model-based approach for detection of load and damage location, and operates based on the time invariance of linear elastodynamic equations. It is shown that using the passive TR scheme, the problem of load and damage detection, which is essentially an inverse problem, can be solved in the form of a forward problem, thereby alleviating uniqueness and stability issues. A number of case studies and examples, numerical and experimental, are presented throughout this dissertation to better demonstrate the applicability of the proposed framework.