The design of a quantitative risk analysis model has to be dictated by the questions it seeks to answer. The model should also be as objective as the available data will allow. Animal and animal product import risks usually have three characteristics which make the design of a good quantitative risk analysis model quite difficult, namely:--the probabilities of the steps leading to the undesired outcome are frequently inter-related--the probability of the undesired outcome itself is in many cases very small, making direct simulation impractical--important variables within the model often cannot be quantified through analysis of data, thus these variables must be modelled with probability distributions to reflect the degree of uncertainty, usually determined by expert opinion. This paper provides a tutorial on some modelling techniques which are essential to the risk assessment of animal and animal product imports and which help overcome these problems. A number of probability distributions, their uses and inter-relationships, are examined. The application of these distributions, coupled with some general modelling techniques, is then demonstrated to produce rigorous and transparent animal import risk analyses.