We develop a model of undescribable events. Examples of events that are well understood by economic agents but are prohibitively difficult to describe in advance abound in real-life. This notion has also pervaded a substantial amount of economic literature. We put forth a model of such events using a simple co-insurance problem as backdrop. Undescribable events in our model are understood by economic agents --- their consequences and probabilities are known --- but are such that every finite description of such events necessarily leaves out relevant features that have a non negligible impact on the parties' expected utilities. We also show that two key ingredients of our model --- probabilities that are finitely additive but fail countable additivity, and a state space that is small (discrete in our model) in a measure-theoretic sense --- are necessary ingredients of any model of undescribable events that delivers our results.