  Motivated by the problem of finding an explicit description of a developable
narrow Moebius strip of minimal bending energy, which was first formulated by
M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently
E.L. Starostin and G.H.M. van der Heijden found a numerical description for an
elastic Moebius strip, but did not give an integrable solution. We derive two
conservation laws, which describe the equilibrium equations of elastic strips.
In applying these laws we find two new classes of integrable elastic strips
which correspond to spherical elastic curves. We establish a connection between
Hopf tori and force--free strips, which are defined by one of the integrable
strips, we have found. We introduce the P--functional and relate it to elastic
strips.
