Popular expositions of the new subject of catastrophe theory have tended to concentrate on ‘soft’ applications, but, as I hope to show, it is perfectly possible to make a serious, important, and mathematically more demanding application intelligible to sixth formers with a minimum of differential calculus. The application is in that part of engineering science which deals with the stability of structures. Catastrophe theory produces nothing really novel in this field, but, by assuming Thorn’s theorem, which will be explained below, it is possible to make the whole subject accessible to those for whom Taylor’s theorem for a number of variables, and the associated concepts, are too difficult. Even for engineers already familiar with the results, catastrophe theory offers an attractive unity within the subject and can point to analogies in related fields.