A distinguishing feature of macro stress testing exercises is the use of macroeconomic models in scenario design and implementation. It is widely agreed that scenarios should be based on "rare but plausible" events that have either resulted in vulnerabilities in the past or could do so in the future. This requirement, however, raises a number of difficult statistical and methodological problems. Economic models, as well as the statistical models of the relationships among economic variables, generally focus on capturing the average rather than the extreme behaviour, and frequently rely on the assumption of linearity. In this paper we show that these models are particularly ill-suited for stress-testing as they do not adequately capture past behaviour in extreme events, nor do they generate plausible responses to shocks under stress. Whereas one might argue that the use of these models is still preferable to no having no models, since they at least impose the consistency restrictions on the paths generated under the scenario, failing to deal with a large extent of uncertainty of these paths may lead to results that are non-informative, and potentially misleading. The paper illustrates both of these problems by a series of examples, but our conclusions have broader implications for the types of models that would be useful in these exercises.