||A structure is vulnerable if small damage could trigger disproportionately large consequence and lead to a cascade of failure events or even collapse. The performance of structural vulnerability depends upon factors such as external loading condition and structural properties. The vulnerability assessment approach in the deterministic and probabilistic domains is developed in this thesis. Typical multi-performance criteria need to be satisfied while conducting such an approach. Approximate method that can capture essential behaviors of structural failure or collapse is favorable in the conceptual design phase for its simplicity and efficiency. In the deterministic domain, vulnerability is defined as the reduction ratio of structural load-carrying capacity against certain performance criterion after a terrorist event. The first approximate method presented in this thesis is for the component yielding criterion. Approximate solution is obtained by constructing a single governing equation, which involves the intrinsic features of the problem and restricts the deformation profiles of cable-stayed bridges with shape functions. The parameters about bridge failure state can be determined by directly using the variational statement. Hence, the bridge load-carrying capacity and vulnerability index can be solved. The vulnerability assessment approach for the single- and twin-pylon cable-stayed bridges is further developed with respect to the ultimate performance criterion, i.e. bridge collapse. The approach is proposed based on the plastic limit analysis method. Some plastic hinge models are constructed respectively for the healthy and initially damaged cable-stayed bridges firstly, so as to derive the geometric properties of the bridge collapse pattern. On the basis of the kinematic theorem of limit analysis, the optimization problem is further built up to solve the parameters about the bridge collapse pattern and its ultimate load-carrying capacity. This approach creates a bridge between approximate method and the best representation of the ultimate behavior that actually occurs during structural failure or collapse. As many factors of engineering structures are random in nature, it is necessary to develop the vulnerability assessment technique in the probabilistic domain. Herein, vulnerability is defined as the system failure probability due to a blast load resulting from a terrorist attack. A vulnerability assessment framework is generated for the cable-stayed bridges, which consists of two stages of analysis: i) determining the probability of direct damage due to uncertain blast loading; and ii) assessing the subsequent probability of collapse. In the first stage, a set of blast reliability curves (BRCs) representing the capacity of a bridge to resist blast loadings was established to calculate the bridge’s failure probability. An event-tree approach is then utilized to analyze the system collapse probability after its initial failure and identify the most critical loading scenario. Through using the proposed deterministic and probabilistic methods, we can gain a better insight into the cable-stayed bridges. It provides a way to improve the original bridge design scheme from the vulnerability point of view, which makes the bridge design to be more safe and reliable.