New imprecise structural reliability models are described in this paper. They are developed based on the imprecise Bayesian inference and are imprecise Dirichlet, imprecise negative binomial, gamma-exponential and normal models. The models are applied to computing cautious structural reliability measures when the number of events of interest or observations is very small. The main feature of the models is that prior ignorance is not modelled by a fixed single prior distribution, but by a class of priors which is defined by upper and lower probabilities that can converge as statistical data accumulate. Numerical examples illustrate some features of the proposed approach.