The elastica theory is a theory of mechanics of solid materials developed by Euler that allows for very large scale elastic deflections of structures. Euler (1744) and Jakob Bernoulli developed the theory for elastic lines and studied buckling. Certain situations can be solved exactly by elliptic functions. Later elastica theory was generalized by F. and E. Cosserat into a geometric theory with intrinsic directions at each point (1907).

Elastica theory is an example of bifurcation theory. For most boundary conditions several solutions exist simultaneously.