Objective measures of animal emotion-like and mood-like states are essential for preclinical studies of affective disorders and for assessing the welfare of laboratory and other animals. However, the development and validation of measures of these affective states poses a challenge partly because the relationships between affect and its behavioural, physiological and cognitive signatures are complex. Here, we suggest that the crisp characterisations offered by computational modelling of the underlying, but unobservable, processes that mediate these signatures should provide better insights. Although this computational psychiatry approach has been widely used in human research in both health and disease, translational computational psychiatry studies remain few and far between. We explain how building computational models with data from animal studies could play a pivotal role in furthering our understanding of the aetiology of affective disorders, associated affective states and the likely underlying cognitive processes involved. We end by outlining the basic steps involved in a simple computational analysis.