Using the concept of total potential energy, V , it is possible to identify four fundamental forms of buckling found in structural models with one degree of freedom. We start by expressing V = U − − P Δ Δ where U is the strain energy stored in the structure, P is the applied conservative load and Δ Δ is the distance moved by P in its direction. Using the axioms of elastic instability theory, namely that equilibrium is any point where V is stationary with respect to the coordinate measuring the degree(s) of freedom and that these points are only stable if V is a local minimum and unstable if otherwise (e.g. maximum or a point of inflection).