The dissertation presents a method developed for assessing the risk to constructed facilities posed by accidental actions. The proposed method is applied to the analysis of structures subjected to accidental actions induced by fire, explosion and extreme wind. The dissertation consists of introduction, five chapters, conclusions, lists of references and papers published by the author of the dissertation, as well as five annexes. Chapter 1 presents a review of published work on the assessment of risk to structures and non-structural property posed by accidental actions. The review covers general aspects of risk assessment and application of risk analysis tools to the analysis and design of structures. The core of the review is an application of Bayesian methods, which prevail in the field of risk assessment, to a risk-based structural analysis. Chapter 2 proposes a method developed for the assessment of damage to structures from accidental actions. This method combines structural analysis with Bayesian handling of information related to accidental actions and response of structures to these actions. The method allows to estimate probabilities of the damage to structures caused by accidental actions. Chapter 3 deals with an application of the proposed method to the estimation of fire risk to structures. It is shown how to apply this method to the estimation of failure probability of a timber beam damaged by fire in an industrial building. This chapter shows how to handle uncertainties in the mathematical model of timber charring and safety margin of the beam. Chapter 4 describes how to apply the proposed method to a design of a safety barrier, which provides protection against an accidental explosion. The accidental action considered in this study is a blast generated by an explosion of a railway tank car. Bayesian modelling of uncertainties is applied to a mechanical model of barrier elements. Chapter 5 presents an application of the proposed method to a case of extreme wind risk assessment. The structure under analysis is a reinforced concrete chimney exposed to a hurricane wind action. The analysis of the chimney takes into account uncertainties related to a mechanical model of this structure.