Since Coulomb's and Saint-Venants fundamental work, many researches have st
udied the effect of twisting on elastic bodies. The work presented here inv
estigates instabilities that can occur when thin bodies are subject to larg
e twists and extends work by A. E. Green published in 1937. Because large t
wists are considered, a fully nonlinear plate theory is used. This theory p
redicts compressive lateral membrane stresses not predicted by Green's weak
ly nonlinear theory. These stresses can significantly alter the twist angle
at which buckling occurs. Two conditions for the opposing twisted end supp
orts are considered. In one case the supports are held a fixed distance apa
rt and in the other case the force applied to the supports is held fixed du
ring twist. The buckling modes and critical twist angles vary significantly
depending on the support condition used.