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A new inextensible theory of beam and plate deformation has been developed. For validation of this inextensible beam and plate theory, computational codes for the static and dynamic nonlinear beam and plate modal equations have been developed. The computations and experiments for static loading and deformation of a beam show that the inextensible theory produces results in excellent agreement with experiment. Also, a comparison of the inextensible theory for a plate with a static experiment is encouraging. Finally, a numerical study of dynamic deflection for an inextensible beam and plate has also been made. The results show a hysteresis dynamic response that depends on whether the excitation frequency is increasing or decreasing for the stiffness nonlinearity only or for the inertia nonlinearity only. The inertia nonlinear force has a significant effect on the dynamic response in the resonant frequency range.