Knowledge in the field of modelling and predicting the dynamic responses of structures is constantly developing. Modelling of uncertainty is considered as one of the tools that increases confidence by providing extra information. This information may then be useful in planning physical tests. However, the complexity of structures together with uncertainty-based methods leads inevitably to increased computation; therefore deterministic approaches are preferred by industry and a safety factor is incorporated to account for uncertainties. However, the selection of a proper safety factor relies on engineering insight. Hence, there has been much interest in developing efficient uncertainty-based methods with a good degree of accuracy. This thesis focuses on the uncertainty propagation methods; namely Monte Carlo Simulation, first-order and second-order perturbation, asymptotic integral, interval analysis, fuzzy-logic analysis and meta-models. The feasibility of using these methods (in terms of computational time) to propagate structural model variability to linear and Computational Fluid Dynamic (CFD) based aeroelastic stability is investigated. In this work only the uncertainty associated with the structural model is addressed, but the approaches developed can be also used for other types of non-structural uncertainties. Whichever propagation method is used, an issue of very practical significance is the initial estimation of the parameter uncertainty to be propagated particularly when the uncertain parameters cannot be measured, such as damping and stiffness terms in mechanical joints or material-property variability. What can be measured is the variability in dynamic behaviour as represented by natural frequencies, mode shapes, or frequency response functions. The inverse problem then becomes one of inferring the parameter uncertainty from statistical measured data. These approaches are referred to as stochastic model updating or uncertainty identification. Two new versions of a perturbation approach to the stochastic model updating problem with test-structure variability are developed. A method based on minimising an objective function is also proposed for the purpose of stochastic model updating. Distributions of predicted modal responses (natural frequencies and mode shapes) are converged upon measured distributions, resulting in estimations of the first two statistical moments of the randomised updating parameters. The methods are demonstrated in numerical simulations and in experiments carried out on a collection of rectangular plates with variable thickness and also variable masses on a flat plate. Stochastic model updating methods make use of probabilistic models for updating same as the perturbation methods developed in this work. This usually requires large volumes of data with consequent high costs. In this work the problem of interval model updating in the presence of uncertain measured data is defined and solutions are made available for two cases. In the first case, the parameter vertex solution is used but is found to be valid only for particular parameterisation of the finite element model and particular output data. In the second case, a general solution is considered, based on the use of a meta-model which acts as a surrogate for the full finite-element/mathematical model. The interval model updating approach is based on the Kriging predictor and an iterative procedure is developed. The method is validated numerically using a three degree of freedom mass-spring system with both well-separated and close modes. Finally the method is applied to a frame structure with uncertain internal beams locations. The procedure of interval model updating, incorporating the Kriging model, is used to identify the locations of the beams at each configuration and to update the bounds of beams positions based on measured data. The method successfully identifies the locations of the beams using six measured frequencies. The updated bounds are found to be in good agreement with the known real bounds on the position of the beams as well.