Similar to linear time invariant systems, modal analysis methods for linear time-varying systems have been developed both in frequency and time domains. However due to the variable nature of these systems with time, use of time-frequency identification methods have been also considered in the recent years. Many well-developed concepts and analytic methods of linear time-invariant systems cannot be applied to linear time varying systems and these system have been often dealt on a case-by-case basis In this thesis, first, according to the modal analysis methods for linear time invariant systems, a time domain method for extracting modal parameters of linear time varying systems is presented and after introducing the procedure, the modal parameters of a beam with moving mass have been extracted and the results are examined. Generally, mathematical theory of the time domain modal analysis methods is complex and difficult to implement. The method presented in this thesis is no exception. In order to introduce an easier approach with higher convergence criteria, Hilbert–Hong transform is presented. Hilbert–Hong transform is a comparative method and in contrast to other time-frequency methods such as wavelet method, is simpler and more capable After introducing a Hilberrt-Hong based method completely, modal parameters of a vibration system are extracted using free and forced vibration response of the system. Empirical mode decomposition is the key point of Hilbert - Huang that extract several intrinsic mode functions from a multi frequency vibration signal. Many linear structural dynamic systems, such as wind turbines, helicopter blades, turbo machinery, and a variety of nonlinear structures linearized about a periodic limit cycle, are modeled with time-periodic coefficients. Linear time periodic systems such as these may exhibit parametric resonance, where the damping in the system is negative at certain rotational frequencies, leading to catastrophic failure. Therefore, modal analysis of these LTP systems has been a main concern for researchers and engineers. A method for extracting modal parameters of linear time-periodic systems in the frequency domain are introduced too. It has been showed that the frequency response function and the assumptions used to determine the frequency response function of linear time invariant systems can not be used for linear time periodic systems. However, using a new frequency space, a frequency response function for a linear time periodic system is introduced and it is shown that, with a combination of this function and frequency domain modal analysis methods for linear time invariant systems, modal parameters of a linear time-varying periodic system can be extracted. At the end, a very preliminary approach is presented to extract the time invariant modal natural frequency of a bridge from modal analysis of the bridge response in the presence of moving vehicles. To perform this analysis a modified homotopy perturbation method is used to relate the natural frequencies of the LTI and LTP responses. Key Words: Beam with Moving Mass, Modal Analysis of Linear Time Varying Systems, Hankel Matrix, Hilbert-Huang Transform, Modified Homotopy Perturbation Method.