The theory proposed in this thesis is an attempt to bridge the gap that exists between the linear and nonlinear theories of Elasticity. The theory is applied to the solution of a hubbed, clamped, circular plate made of polyurethane whose hub is subjected to a "large" axi~symmetrioc twist. This particular problem is attacked in the conventional manner of the generalized plane stress problem of linear elasticity. However, the strain displacement relations are formulated in the Eulerian manner and the displacement gradients are not assumed to be small. In addition, a more general stress~strain relationship than the conventional Hookean form is assumed. The solution is checked by experiment; and in addition, three auxiliary problems; the uniaxial compression problem, the uniaxial tension problem, and a shear problem are checked experimentally to further cheek the validity of the proposed theory when applied to the finite strain response of polyurethane. / Ph. D.