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Noise, vibration and harshness (NVH) is of increasing concern for the automotive and aerospace industries, due to the desire for new materials and lighter structures and the increasing use of sensitive on-board electronics. Finite element analysis (FEA) and statistical energy analysis (SEA) are popular and well-established numerical simulation methods for NVH analysis in the low- and high-frequency range, respectively. However for the mid-frequency range, there is no readily available method to handle the vibration analysis of the full complex structure in a systematic fashion with acceptable efficiency and accuracy relative to a lower or higher frequency region. Thus, the mid-frequency range is regarded as one of the last frontiers in linear structural dynamics, and the search for vibration analysis methods for the mid-frequency range remains active and intense. The work presented in this dissertation is based on FEA and component mode synthesis (CMS), and the focus is on improving the capabilities of FEA- and CMS-based methods and pushing the scope of their applications up into the mid-frequency range. Computational cost is a major limiting factor for using FEA and CMS in the mid-frequency range. Therefore, in this dissertation, major improvements are made to CMS to achieve better efficiency. First, an interface reduction method is employed to obtain a more compact reduced-order model (ROM), so that further dynamic analysis based on the ROM, such as forced vibration response and power flow analysis, can be performed with better efficiency. Second, a matrix-filtration method is applied to improve the efficiency of both substructure analysis and interface reduction. Third, quasi-static modes are used to construct a highly compact ROM for dynamic analysis in the mid-frequency range. Another key issue for FEA and CMS in the mid-frequency range is the significant effect of parameter uncertainties on the dynamic response. Therefore, in this dissertation, the CMS method is further integrated with a parametric modeling approach to obtain a component-based parametric reduced-order modeling method. Numerical results are presented for applications to both simple models and complex vehicle models. It is shown that the proposed methods can handle probabilistic vibration analysis and design of complex structural models in both the low- and mid-frequency range, with impressive efficiency and accuracy.