In this work, the random vibration of higher-order nonlinear beams and composite plates subjected to stochastic loading is studied. The fourth-order nonlinear beam equation is examined to study the effect of rotary inertia and shear deformation on the root mean square values of displacement response. A new linearly coupled equivalent linearization method is proposed and compared with the widely used traditional equivalent linearization method. The new method is proven to yield closer predictions to the numerical simulation results of the nonlinear beam vibration. A systematical investigation of the nonlinear random vibration of composite plates is conducted in which effects of nonlinearity, choices of different plate theories (the first order shear deformation plate theory and the classical plate theory), and temperature gradient on the plate statistical transverse response are addressed. Attention is paid to calculate the R.M.S. values of stress components since they directly affect the fatigue life of the structure. A statistical data reconstruction technique named ARMA modeling and its applications in random vibration data analysis are discussed. The model is applied to the simulation data of nonlinear beams. It is shown that good estimations of both the nonlinear frequencies and the power spectral densities are given by the technique. / Ph. D.